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March 12th, 2017, 08:56 PM   #1
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Finding the Critical point

Consider the following function.

g(x, y)  =  e− 8x^2 − 6y^2 + 24 y

(a) Find the critical point of g.

(b) Using your critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point.

(c) Use the Second Partials test to classify the critical point from (a).

I could really use some help on finding the critical point. i'm not sure where to start.
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 March 12th, 2017, 08:59 PM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 923 Thanks: 499 can you find the partial derivatives $\dfrac{\partial g(x,y)}{\partial x}$ and $\dfrac{\partial g(x,y)}{\partial y}$ critical points occur where both these quantities are equal to zero. For the rest of it look here
 March 13th, 2017, 10:58 AM #3 Newbie   Joined: Mar 2016 From: Canada Posts: 21 Thanks: 0 I got the first part of the question g(x,y)=exp(−8x2−6(y−2)2+24)≤exp(24)=g(0,2) but how do part b?
March 13th, 2017, 11:13 AM   #4
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Quote:
 Originally Posted by puppypower123 I got the first part of the question g(x,y)=exp(−8x2−6(y−2)2+24)≤exp(24)=g(0,2) but how do part b?
did you look at the link?

You compute the Hessian matrix and find it's determinant at the critical point to try and classify it.

Last edited by romsek; March 13th, 2017 at 11:19 AM.

March 13th, 2017, 12:22 PM   #5
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Quote:
 Originally Posted by puppypower123 Consider the following function. g(x, y)  =  e− 8x^2 − 6y^2 + 24 y
You mean e to the power of -8x^2- 6y^2+ 24y!
You have already written powers with "^"so why did you not write
g(x,y)= e^(-8x^2- 6y^2+ 24)?

Quote:
 (a) Find the critical point of g.
A "critical point" is defined as a point where the partial derivatives either do not exist or are 0. Have you found the partial derivatives?

Quote:
 (b) Using your critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point.
D(a, b) is defined as $f_{xx}(a, b)f_{yy}(a,b)- f_{xy}^2(a, b)$

Quote:
 (c) Use the Second Partials test to classify the critical point from (a).
Okay, what is the "second partials test"?

Quote:
 I could really use some help on finding the critical point. i'm not sure where to start.
Start by taking a Calculus class or at least reading a Calculus text book!

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