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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:14:52
cos(x)cos(y)=0
1
0
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null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:01
-sin(x)sin(y)=0
1
0
null
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null
null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:09
https://cdn.discordapp.c…3280/unknown.png
unknown.png
1
0
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null
null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:20
i get expression for saddle max min points looks like
1
0
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null
null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
880,503,100,711,010,300
Rylo
02/20/2022 07:15:20
you can expand that
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
880,503,100,711,010,300
Rylo
02/20/2022 07:15:32
to get this
0
1
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null
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:32
i know i unexpanded that
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:35
yes
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:15:44
but if i do it like this i get correct expression
1
0
880,503,100,711,010,300
Rylo
1068
Rylo
false
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:16:35
Like ( x - y ) = π/2 is one such plane where cos( x - y ) = 0 And, f(x, y) = (sin x)^2 in this plane
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:16:54
maximize this and you have 1 as maximum value
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:17:15
now pick (x - y) = 3π/2
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:17:38
you'll have f(x, y) = - (sin x)^2 in this plane
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:17:48
minimize and you have -1 (@_@;)
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
880,503,100,711,010,300
Rylo
02/20/2022 07:18:15
get a load of you matey
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:18:25
lmao
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:18:56
but yeah, can see this working graphically
0
1
312,581,003,095,048,200
Akintos
5593
Akintos
false
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:19:35
what did those sinuses come from
1
0
312,581,003,095,048,200
Akintos
5593
Akintos
false
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:22:15
optimizing the function in the plane where gradient of curve zero
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:24:37
😳
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:26:18
wha-
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:26:19
+_+
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:28:06
I understood nothing
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:32:46
z = f(x, y) is the 3-D thingy right?
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:33:12
ye
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:33:14
so, the minimum/maximum value occurs at z = z_0 right ✓
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:33:24
at this point the gradient = 0 ✓
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:33:44
yeah
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:35:57
that's why I used the condition
0
1
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:36:24
and optimised the function on places where gradient = 0? 🤔
0
1
706,934,233,012,371,600
Ansh_
3502
Arya
false
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:37:40
hmm ait
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:40:10
so in the end how was i supposed to use it
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:40:22
cuz there was a lot of back and forth and i got sompletely confused sry lol
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:40:44
no worries (ヘ・_・)ヘ┳━┳ I don't know the answer to that either
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:41:02
maybe time to call the @Helpers
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:41:19
https://cdn.discordapp.c…80/unknown-7.png
unknown-7.png
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:41:46
how to use the method of Lagrange Multipliers with inequality constraints?
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:53:59
or
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 07:54:04
solve this one in general
0
1
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 07:55:30
cos(x-y) =0 looks right
0
1
null
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 07:56:44
Now just like x-y= +/- pi/2 or 3pi/2, and substitute into x+y= 2pi
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 07:59:17
this gives coordinates on the intersection
1
0
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 07:59:58
You plug those back to get the values
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:00:12
what
1
0
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:00:53
Like after you get the coordinates
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:01:13
You put them into f(x,y)
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:01:29
https://cdn.discordapp.c…8480/unknown.png
unknown.png
1
0
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null
null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:01:44
those are not the correct max or min x,y coordinates
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:02:42
There are 3 other cases
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:02:55
^
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:03:30
Actually you can ignore the negative ones I think
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:03:38
So 3pi/2
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:04:16
none of those are correct
1
0
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786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:05:15
Yeah, optimizing along the line doesn't give the max or min
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:05:16
Anyways
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:05:25
I got this
https://cdn.discordapp.c…20220-WA0004.jpg
IMG-20220220-WA0004.jpg
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:05:31
:o
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:06:10
yeah i used it on previous questions but it just helps to identify what a set point is
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:06:16
we dont even get the correct points
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:06:23
You would though-
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:06:44
$\cos x \cos y = 0 \land \sin x\sin y = 0$
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
510,789,298,321,096,700
TeXit
02/20/2022 08:06:47
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
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null
null
null
786
help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:06:53
Honestly id just put y=2pi-x and differentiate
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:07:07
which would again, give you the wrong answers...
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:07:23
I said, solving along the line isn't giving the correct answer
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:07:24
smh
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:07:46
Oh wait it's the bounded region
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:07:50
Yes
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
714,483,444,394,229,900
Frosty_
02/20/2022 08:07:56
I'm dumb
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:09:24
i guess i will just ask the lecturer
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:09:33
Please do
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:09:44
I strongly believe it's using this though
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:09:50
:this:
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1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:10:24
$\cos x \cos y = 0 \land \sin x\sin y = 0$
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
510,789,298,321,096,700
TeXit
02/20/2022 08:10:27
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
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null
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:10:41
i have to wait untill wednsay to ask him doe, annoying i wanted to be done early
1
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:10:48
so either $\cos x = 0, \sin y = 0$ or $\sin x = 0, \cos y = 0$
0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
510,789,298,321,096,700
TeXit
02/20/2022 08:10:50
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:11:08
This gives 8 pairs of critical points
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:11:53
i mean yeah, i found the critical points like this
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:11:56
but then theyre not bound
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:12:18
and if i get a question like this i cant really look at the graph and shuffle thru points to check which ones fit my constraint
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
510,789,298,321,096,700
TeXit
02/20/2022 08:12:59
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:13:00
AND
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
510,789,298,321,096,700
TeXit
02/20/2022 08:14:01
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:14:20
They're all the critical points **within the bound**
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:14:43
what how did you find them
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:15:03
partial derivative w.r.t. x and y equal zero :akko_lewd:
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:15:51
but how did you only get the ones that are bound??
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:15:58
Handpicked them?
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:16:31
well the whole reason i wanted to do lagrange is so i wouldnt have to handpick then when i have little time on the exam 🙃
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:16:41
lmfao
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:17:01
takes only 10 secs max to reject solutions not within the bound
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:17:10
there's only two points out of bound anyways
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
312,581,003,095,048,200
Akintos
02/20/2022 08:17:37
hm i guess so
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:18:08
**ALSO** if you're ONLYYYYY interested about the optimization thingy for MCQs
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:18:20
You could now just plug in the values ✓
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:18:41
Note: x = 0 would give f(x, y) = 0 which is not really the min / max
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:19:06
reject the whole second solution set where sin x = 0, cos y = 0
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help-10
cb65cd960cf741f4b7303617f2d4ecb6
706,934,233,012,371,600
Ansh_
02/20/2022 08:19:39
evaluate at first set of points and you have your critical points where min. and max. occurs
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