My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 12th, 2017, 08:56 PM   #1
Newbie
 
Joined: Mar 2016
From: Canada

Posts: 21
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
File Type: jpg qq1.jpg (17.7 KB, 0 views)
puppypower123 is offline  
 
March 12th, 2017, 08:59 PM   #2
Senior Member
 
romsek's Avatar
 
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
romsek is online now  
March 13th, 2017, 10:58 AM   #3
Newbie
 
Joined: Mar 2016
From: Canada

Posts: 21
Thanks: 0

Question

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?
puppypower123 is offline  
March 13th, 2017, 11:13 AM   #4
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 923
Thanks: 499

Quote:
Originally Posted by puppypower123 View Post
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.
romsek is online now  
March 13th, 2017, 12:22 PM   #5
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,279
Thanks: 570

Quote:
Originally Posted by puppypower123 View Post
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

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!
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
critical, finding, point



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Question regarding a critical point formula MFP Calculus 6 August 21st, 2013 02:42 PM
Finding Critical Points? allylee Calculus 1 October 21st, 2012 10:26 PM
Critical point felicia184 Calculus 5 September 17th, 2012 10:05 AM
Non-Linear First Order ODE: Critical Point Linearization Mike86 Applied Math 2 October 9th, 2010 06:02 AM
Critical point felicia184 Algebra 0 January 1st, 1970 12:00 AM





Copyright © 2017 My Math Forum. All rights reserved.