context stringlengths 545 71.9k | questionsrc stringlengths 16 10.2k | question stringlengths 11 563 |
|---|---|---|
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | so could the quadratic formula replace factoring overall ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative w... | area of a rectangle is 225m^2 and perimeter is 60 m way is the length ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | you know , whenever c is zero and you use the quadratic formula , does n't that automatically make the origin ( 0 , 0 ) a zero for that function ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | while the quadratic formula can be used for quadratic equations , can it be used in quadratic inequalities ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | can you use the quadratic formula to find an output of a number that is n't zero ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's nice . that 's a nice perfect square . all of that over 2 , and so this is going to be equal to negative 4 plus or minus 10 over 2 . | with the quadratic equation why do n't i find the correct x values when i try to solve it with the perfect square approach ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | when graphing quadratic equations and also using the formula we look for x , would there be a formula for finding the y intercepts ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | what is a real-life situation where someone would need to know the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . | does the +/- indicate an ( and ) relationship or an ( or ) relationship ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of those numbers . so this actually does have solutions , but they involve imaginary numbers . so this actually has no real solutions , we 're tak... | i 'm pretty rust on my math , in the second example with no real solutions , is the imaginary solution -1 +/- 2i sqrt ( 21 ) ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | let 's rewrite the formula again , just in case we have n't had it memorized yet . x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem . | could n't you ( or why could n't you ) simplify part of the formula from 'plus or minus the square root of b squared minus 4ac ' to just 'b minus 4ac ' ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared . b is 6 , so we get 6 squared minus 4 times a , which is 3 times c , which is 10 . | does n't the square root cancel out the extra b ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | why do we need the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | and now we can use a quadratic formula . so let 's apply it here . so a is equal to 3 . | is there a difference if i apply the ruffini rule ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 . | i.e -4.9 ( x-4 ) +50 = 0 then how do we expand and plug in quadratic ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . | in specfically where did -3 come from ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times... | and what happened to the 2 in the next step from 2 times the sqaure root of 39 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? | when putting an already negative number into a negative variable in the formula , do you make the number positive or keep it negative ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . | for example the quadratic 3x^2-3x-5 , when putting -3 in to the negative -b variable in the quadratic formula , do you make it 3 or -3 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | and let 's just plug it in the formula , so what do we get ? we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? | for example , if i have the equation f ( x ) =x^2-18x+86 , when i plug it into the quadratic formula with a negative b , do i change my b to a postive because it is already negative , or does it have to be a negative either way ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so once again , the quadratic formula seems to be working . let 's do one more example , you can never see enough examples here . and i want to do ones that are , you know , maybe not so obvious to factor . | what is the meaning of having two or more answers for one equation or one expression ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | when should you use the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times... | @ 13.37 what happened to + - 2 before square root 39 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that with that -- since this is the first time we 're doing it , let me not skip too many steps . | i am really confused on what is happening ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's a nice perfect square . all of that over 2 , and so this is going to be equal to negative 4 plus or minus 10 over 2 . we could just divide both of these terms by 2 right now . so this is equal to negative 4 divided by 2 is negative 2 plus or minus 10 divided by 2 is 5 . so that tells us that x could be equal to... | what do i do in order to answer the equations 4b^2+8b+7=4 and 5r^2=80 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | and the reason why it 's not giving you an answer , at least an answer that you might want , is because this will have no real solutions . in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of thos... | how many trees should be planted to produced a maximum number of mangoes per year ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . | i mean , the roots are the values of x for when y is zero , right ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so that 's the equation and we 're going to see where it intersects the x-axis . where does it equal 0 ? so let me graph it . | so why is it that in the quadratic , the solutions are only for when y = 0 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | and let 's just plug it in the formula , so what do we get ? we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . | when you do b ^ how come you do not add in the x ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | and let 's just plug it in the formula , so what do we get ? we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . | b being 12 x , why is it not 144 x , but only 144 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . | why is it that when you plugged them into the formula , at the square root , could you put those numbers into parenthesis instead of using the dot ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . | if b is negative in the starting equation would you make it positive in when it says -b in the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | well , the first thing we want to do is get it in the form where all of our terms or on the left-hand side , so let 's add 10 to both sides of this equation . we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | how would i solve a problem like 3x^2-12=0 using the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . | what happend to the +-2 behind the ( 39 ) ^1/2 when the top half was being devided by -6 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | let 's do one more example , you can never see enough examples here . and i want to do ones that are , you know , maybe not so obvious to factor . so let 's say we get negative 3x squared plus 12x plus 1 is equal to 0 . | how does i know if the graphic needs to go up between the points and go down between the points ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | a negative times a negative is a positive . so once again , you have 2 plus or minus the square of 39 over 3 . 2 plus or minus the square root of 39 over 3 are solutions to this equation right there . let verify . | 1is 2 plus or minus the square root of 26 an ok answer ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | how can you find the nature of the roots using the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | how can you find the nature of the roots using the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? | what if b is already negative ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | its vertex is sitting here above the x-axis and it 's upward-opening . it never intersects the x-axis . so at no point will this expression , will this function , equal 0 . | what if when you graph the equation and very bottom part goes below the x-axis ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | hi can some one tell me what previous math i need to know in oder to understand the quadratic formula ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times... | how does it come out to the square root of 2 times 2 multiplied by the square root of the 39 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative will become positive . | when sal takes out the 2 , why is the -12 also affected and reduced to -6 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | why does the quadratic formula have to be so long is n't there a simpler way ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared . b is 6 , so we get 6 squared minus 4 times a , which is 3 times c , which is 10 . | for example how do you know that 6x represents the b ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that is a , this is b and this right here is c. so the quadratic formula tells us the solutions to this equation . the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared . | how do you find the explicit/recursive equation for a quadratic function ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | in `` quadratic formula '' practice problems , why does it seem that the coefficient on radicals is ignored ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . | what is the dimension of the largest total area martin can enclose ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . 2 square roots of 39 , i... | in the last few minutes , how was the 2 before the square root removed ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we could just divide both of these terms by 2 right now . so this is equal to negative 4 divided by 2 is negative 2 plus or minus 10 divided by 2 is 5 . so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 . | considering the way quadratic equations are written , when adding 10 to the left side if i were to replace 3x^2 with 10 , make the b term 3x^2 and make the c term 6x , would that affect the solution of the answer ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | it 's worthless . it just gives me a square root of a negative number . it 's not giving me an answer . | what happens when u have a negetive number under the sq root ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? | how does the b work if it is already a negative ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared . b is 6 , so we get 6 squared minus 4 times a , which is 3 times c , which is 10 . | when you have x=-b ... .if the b is already a negative then is it x=b ... , or is it always x=-b ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | let me rewrite this . so this right here can be rewritten as 2 plus the square root of 39 over negative 3 or 2 minus the square root of 39 over negative 3 , right ? that 's what the plus or minus means , it could be this or that or both of them , really . | is our final answer 2 plus/minus the square root of 39 over 3 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so negative 21 , just so you can see how it fit in , and then all of that over 2a . a is 1 , so all of that over 2 . so what does this simplify , or hopefully it simplifies ? | this also begs another question ... does a second order polynomial really descend by 1/2 or does it de-increment by 1 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so once again , you have 2 plus or minus the square of 39 over 3 . 2 plus or minus the square root of 39 over 3 are solutions to this equation right there . let verify . | what is the positive root in an equation ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem . let 's say we have the equation 3x squared plus 6x is equal to negative 10 . | when doing a quadratic formula problem with a negative in the radical , how do you solve such problem ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . | 3x^2=39 what formula is used to solve the equation ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . | is n't there a small mistake at 1? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? | wait ... if the formula says b^2 minus 4ac , why did mr sal put an addition sign ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . | does the sign change for x ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . | how come we are solving for x ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | or we could separate these two terms out . we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? | could you have just did negative 12 divided by negative 6 and got 2 plus or minus square root of 39 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . | why not just find the square root of 156 to make things much easier ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared . b is 6 , so we get 6 squared minus 4 times a , which is 3 times c , which is 10 . | would n't using the slope intercept form `` y=mx+b '' and putting that in your graphing calculator be a better way to solve ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . | what is the square root of 11,390,881 ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | so once again , the quadratic formula seems to be working . let 's do one more example , you can never see enough examples here . and i want to do ones that are , you know , maybe not so obvious to factor . | what exactly is the concept of `` one repeated solution '' ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here . | what is the use of the quadratric formula in the sat ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . | what would you get for 2x-5=-x squared ? |
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau... | b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that with that -- since this is the first time we 're doing it , let me not skip too many steps . | why are all the comments from 4 years ago ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | and when those liquid sodium ions come in contact with those electrons , we get a reduction half-reaction , so let me write , this is a reduction half-reaction . sodium ions gain electrons , and are reduced to form liquid sodium metal . so liquid sodium metal is one of our products . | why do sodium ions gain two electrons instead of one ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | if we have moles of sodium , how does that help us find our charge ? well , we can relate the moles of sodium to the moles of electrons . so let 's go back up here to our half-reaction where we have our moles of sodium . | can you just use the equation moles = current * time / faraday 's constant * moles electrons for the kind of problem presented around 3 ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | we can also figure out how many liters of chlorine gas are produced when we make our sodium . so let 's say we 're at stp here , so standard temperature and pressure . remember , standard temperature is zero degrees c , and standard pressure is one atmosphere . | is it realistic to ask how much cl2 is produced at stp given molten nacl would be at a far higher temperature and/or pressure than 0oc and 1.0atm ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | and when those liquid sodium ions come in contact with those electrons , we get a reduction half-reaction , so let me write , this is a reduction half-reaction . sodium ions gain electrons , and are reduced to form liquid sodium metal . so liquid sodium metal is one of our products . | how does electrons from chlorine reaches sodium ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . | are n't positive ions called cations ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | so chloride anions , liquid chloride anions are oxidized to chlorine gas , so we lose two electrons . so chloride anions are oxidized to chlorine gas at the anode , and so we 'd have bubbles of chlorine gas forming at this electrode . this is an important reaction in industry . | why does n't sodium react with chlorine gas again ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | how long does it take to produce 1.00 times 10 to the third kilograms of sodium , so that 's a lot of sodium , with a constant current of 3.00 times 10 to the fourth amps . so we have another quantitative electrolysis problem here . this one 's a little bit harder than the one we did before , but we 're going to start ... | is electrolysis of water endothermic or not ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | we 're trying to find the volume , we 're trying to find liters , so we 're trying to find v , n would be equal to the number of moles , so that would be 21,750 , so we have 21,750 moles . r , r is equal to .0821 ... and i did n't leave room for the units in there . but the units would cancel out to give us liters for ... | same ques for formation of n2 from n atom ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . | what kind of material must have the electrodes for electrolysis molten salt ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | the other half-reaction , at our other electrode , we know that our battery draws electrons away from this electrode . so oxidation is occurring at this electrode . this would be the anode . so chloride anions , liquid chloride anions are oxidized to chlorine gas , so we lose two electrons . | how would you go about figuring which species undergoes reduction or oxidation if the solution is aqueous instead of molten ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | and when those liquid sodium ions come in contact with those electrons , we get a reduction half-reaction , so let me write , this is a reduction half-reaction . sodium ions gain electrons , and are reduced to form liquid sodium metal . so liquid sodium metal is one of our products . | why does sodium gains an electron , sodium has an extra electron already ? |
here 's a simplified diagram for the electrolysis of molten sodium chloride . so if you melt solid sodium chloride , you get molten sodium chloride . so you get sodium ions , liquid sodium ions , and you get liquid chloride anions . so that 's what we have here , we have sodium ions and chloride anions . remember , in... | so chloride anions , liquid chloride anions are oxidized to chlorine gas , so we lose two electrons . so chloride anions are oxidized to chlorine gas at the anode , and so we 'd have bubbles of chlorine gas forming at this electrode . this is an important reaction in industry . | it makes chlorine gas while making metal right ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | so isovolumetric , same volume . so contraction . and all that means is that hey , the left ventricle 's contracting . | how much do the relative proportions of contraction and relaxation discussed in the video change with rising heart rate ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | but the truth is that we have to remember that the left ventricle is relaxing during this time . and diastole is all about relaxation for the left ventricle . so because it 's part of relaxation , it is technically and truthfully part of diastole , even though it looks like it 's part of the lump . | during the second half part of the yellow line ( at the top ) , there is relaxation of the ventricles therefore the left ventricle pressure drops , then why it is considered under the systole at the end of the video ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | because the whole point is that this is all happening in about a second . and that 's if we assume , of course , that our heart rate is 60 beats a minute . now , that is not always true , of course . | can you explain me about right ventricle of heart and about heart beat ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . | how to draw right ventricular and atrial pressure curve ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . | can you explain me why did you put the ( atrial ) systole in the curve left ( ventricular ) curve , please ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | so this is where the valve now says , hey , enough is enough . let 's shut down , because pressure is going the other way . and then , our blood pressure is going to fall . it 's going to fall , and it 's going to fall over a bit of time . | is the temperature of the blood going up during this time with the two valves closed , pressure going up but volume staying the same ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | let 's shut down , because pressure is going the other way . and then , our blood pressure is going to fall . it 's going to fall , and it 's going to fall over a bit of time . | i am confused by the pressure in the graph , is it the force exerted by the ventricles or the pressure by the blood on the ventricles ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | so this part right here , this third segment , where i 'm going to use green , again you have the aortic valve is closed , but the mitral has not yet opened . and so does blood have anywhere to go ? nope . | in the part of isovolumetric relaxation u said that the blood has no where to go ... now where does that blood come from if the ventricle has just finished contracting and pushing blood into the aorta ? |
so the main thing i wanted to do in this video is just show you the timing of a heartbeat . and we 've been drawing the left ventricular pressure . and so far , i 've just sketched it out . but now , i want to try to be a little bit more careful with how i draw it so that you can get a real appreciation for how long ev... | it 's always open . but the aortic valve opened at that point . now , between those two -- and this is actually really a cool thing to think about -- between those two , what 's going on ? | or there is some blood that remains in the ventricle even after contarction is over and aortic valve shuts ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | but then when we go over here , even though the value of our function has gone down , we still have a constant positive slope . in fact , the slope of this line looks identical to the slope of this line . let me do that in a different color . | why does n't sal shade in the yellow circle ( which marks the beginning of the red line ) 4 ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | so i would draw it right over there . so it 's a weird looking function . but the whole point of this video is to give you an intuition for thinking about what the slope of this function might look like at any point . and by doing so , we have essentially drawn the derivative over that interval . | is the tangent line the derivative of the function at the certain point ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | but the whole point of this video is to give you an intuition for thinking about what the slope of this function might look like at any point . and by doing so , we have essentially drawn the derivative over that interval . | is there a case in which we have a curve in the derivative , or are there only lines ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . | whats the difference between the shaded and not-shaded circles ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | but then when we go over here , even though the value of our function has gone down , we still have a constant positive slope . in fact , the slope of this line looks identical to the slope of this line . let me do that in a different color . | around sal draws a open dot to start the blue line - should n't it be closed because we know it 's zero ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | we have a line with a constant positive slope . so it might look something like this . and let me make it clear what interval i am talking about . | 0 , should the graph of the derivative resemble something like the graph of tangent ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | and then we go up here . the value of the function goes up , but now the function is flat . so the slope over that interval is 0 . | why is the derivative of second and third function a horizontal line ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | now let 's think about as we get to this point . here the slope seems constant . our slope is a constant positive value . so once again , our slope here is a constant positive line . let me be careful here because at this point , our slope wo n't really be defined , because our slope , you could draw multiple tangent l... | so does the y-axis on the lower graph represent the slope of the tangent lines ? |
so i 've got this crazy discontinuous function here , which we 'll call f of x . and my goal is to try to draw its derivative right over here . so what i 'm going to need to think about is the slope of the tangent line , or the slope at each point in this curve , and then try my best to draw that slope . so let 's try ... | let me be careful here because at this point , our slope wo n't really be defined , because our slope , you could draw multiple tangent lines at this little pointy point . so let me just draw a circle right over there . but then as we get right over here , the slope seems to be positive . | why does sal not shade in the second blue circle ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.