My Math Forum Finding the Critical point
 User Name Remember Me? Password

 Calculus Calculus Math Forum

March 12th, 2017, 08:56 PM   #1
Newbie

Joined: Mar 2016

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.
Attached Images
 qq1.jpg (17.7 KB, 0 views)

 March 12th, 2017, 08:59 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,500 Thanks: 1372 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: 2,500
Thanks: 1372

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
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

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!

 Tags critical, finding, point

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post MFP Calculus 6 August 21st, 2013 02:42 PM allylee Calculus 1 October 21st, 2012 10:26 PM felicia184 Calculus 5 September 17th, 2012 10:05 AM Mike86 Applied Math 2 October 9th, 2010 06:02 AM felicia184 Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top