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NationalTutoringObservatory
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MathEd-PII

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volunteer
there is a local maximum at the tip of each ^ and a local minimum at the bottom of each V
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student
I will be right back
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volunteer
ok!
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student
I'm back
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volunteer
Great!
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volunteer
Did that explanation make sense?
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student
yes
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volunteer
Ok good!
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volunteer
Do you have any ideas where the local minimums of that graph might be?
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volunteer
Yep!
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volunteer
Now this question asks what the local minimum values are
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volunteer
this means it is asking for the y-value
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volunteer
and since these points both have the same y-value, the answer to the question should only be 1 number
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volunteer
Do you know what the y coordinate of these local minimums is?
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student
-2
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volunteer
Yes!
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volunteer
Great job!
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volunteer
Now the next question is asking where the graph has a value that is a local minimum
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volunteer
this means it is asking for the x coordinate of the local minimums
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student
4 and 0
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volunteer
The 1st question asks what the local minimum values are, meaning it is asking how low the graph gets at its local minimums which means it is asking for the y coordinate since that is the coordinate that determines how high/low the point is
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volunteer
Yes!
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volunteer
The 2nd question is asking where the graph has those y-values, which means it is asking for the x-values
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volunteer
Those types of questions can be confusing because it is hard to tell ig they are asking for the x or y coordinate
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volunteer
but you are correct the answer is 0 and 4!
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volunteer
Do you need help with anything else?
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student
no
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volunteer
Ok! should I end the session then?
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student
ok
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volunteer
Ok! Goodbye!
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student
hi
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volunteer
Hii how can I help
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volunteer
OK. Um
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volunteer
can you tell me which are the local minimums of G?
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volunteer
Do you need help with understanding the concept?
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student
yes
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volunteer
Would you like me to explain what a local minimum of function is.
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student
yes please
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volunteer
OK, great. Um.
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volunteer
OK, let me try to
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volunteer
hm, clear it out for you. Um, if you want to find where the function has a local minimum, you have to look at the function, the lowest points in a certain um sector of the function.
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volunteer
For example
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volunteer
um, for G,
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volunteer
um
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volunteer
you have to look where the function changes from decreasing to increasing, like the valleys of the graph.
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volunteer
Um, for G, it's -2. You know why? Because from -4 to -1, the function is decreasing and the minimum points of the function is that
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volunteer
X equals -2.
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volunteer
So let me just write that down.
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volunteer
When
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volunteer
Did you understand what I explained or
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volunteer
would you like me to elaborate?
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student
yes
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volunteer
Great. Now, can you find the other local minimums of dysfunction.
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volunteer
based on this example
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volunteer
Actually, what you just found, uh, the point that you pointed out is the local maximum of the function because at this point of the curve, the curve has its maximum value, which is coming from -5 to -2.
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volunteer
Here it's the maximum value that minus 4 that you pointed. You need to find the point of the curve when it's the minimum, the lowest point.
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volunteer
For example, um, X equals 0, where Y equals 3, that's also a maximum point.
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volunteer
You should try finding the minimum point.
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volunteer
Yes, exactly. That's another
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volunteer
local minimum point of G.
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volunteer
Now, the local minimum value of G is another thing.
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volunteer
It wants you to put the local minimum value of X, the one you found is in X equals 3 and x equals minus 2.
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volunteer
Am I seeing that right? Is it -2 or minus, yeah, -2.
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volunteer
You put this value of X and you find the value of why in that specific point.
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volunteer
For example, for x equals minus 2. Let me type that down.
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volunteer
x=-2
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volunteer
then y=-1
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volunteer
Now, based on this example, can you find the, the other local minimum value of G.
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volunteer
Would you like me to explain it once again?
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student
yes
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volunteer
OK, let me try and be more specific. So you find, found the minimum values, the local minimum values of G, which were minus 2 and -3, right?
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volunteer
These are the values of X.
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volunteer
on the graph.
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volunteer
A point has two coordinates. Those are X and Y.
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volunteer
So, if a question asks all values at which G has local minimum, it wants the values of X.
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volunteer
But when the question asked all local minimum values of G, it wants the values of y.
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volunteer
Um
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volunteer
so
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volunteer
for this graph, for graph G,
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volunteer
uh the minimum value, one of the minimum values was minus 2 and the other one was 3.
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volunteer
So when you look at this point,
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volunteer
this point in -2, can you say what is its Y coordinate?
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volunteer
You should just look at the graph.
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volunteer
and at the scale of y.
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volunteer
and just say the corresponding coordinate.
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volunteer
can you tell me the coordinates of the red dot
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volunteer
do you know what coordinates mean?
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student
yes
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volunteer
okay great
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volunteer
now find the coordinates of the red dot
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student
(-2,-3)
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volunteer
yeah that's correct
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volunteer
that is what the question needs
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volunteer
Now you found the coordinates for the dots, and you remember that -2 was the uh value where G has a local minimum.
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volunteer
So you have your first answer for the first question.
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volunteer
The other coordinates, the other dots that we found was this one.
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volunteer
where X equals 3.
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volunteer
Can you find the Y value of this dot as well.
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student
0
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volunteer
Yes, this is also correct. So now we've found both X's and Y coordinates of the local minimum points of the function, and that's all the question wanted.
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