March 12th, 2017, 08:56 PM  #1 
Newbie Joined: Mar 2016 From: Canada Posts: 24 Thanks: 0  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. 
March 12th, 2017, 08:59 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,977 Thanks: 1026 
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: 24 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  
Senior Member Joined: Sep 2015 From: USA Posts: 1,977 Thanks: 1026  Quote:
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  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,194 Thanks: 871  Quote:
You have already written powers with "^"so why did you not write g(x,y)= e^(8x^2 6y^2+ 24)? Quote:
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