Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Second Derivative Test: Classifying Critical Points of Given Functions, Assignments of Analytical Geometry and Calculus

University of Nebraska–Lincoln (UNL)Analytical Geometry and Calculus

The answers to the additional problems of the second derivative test in math 208. The functions' critical points are classified as local maxima, local minima, or saddle points.

Typology: Assignments

Pre 2010

Uploaded on 08/30/2009

koofers-user-14d-1
koofers-user-14d-1 🇺🇸

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 208
Second derivative test additional problems
Find and classify (as local maxima, local minima, or saddle points) the critical points of
the following functions.
1.
2 2 2
( , ) 8 4 7
f x y x x y y
= + + −
2.
2 2
( , ) 2 2
f x y yx y x xy
= − +
3.
3 4 2
( , ) 4 8 2
f x y y y xy x
= − + −
4.
2 2
54
( , ) 9
f x y x y
= + −
pf2

Partial preview of the text

Download Second Derivative Test: Classifying Critical Points of Given Functions and more Assignments Analytical Geometry and Calculus in PDF only on Docsity!

Math 208 Second derivative test additional problems Find and classify (as local maxima, local minima, or saddle points) the critical points of the following functions.

2 2 2 f ( , x y ) = 8 x + 4 x y + y − 7

2 2 f ( , x y ) = yx − 2 y x + 2 xy

3 4 2 f ( , x y ) = 4 y − y + 8 xy − 2 x

(^2 2 ) ( , ) 9 xy f x y = x + y −

Answers:

  1. Local min at (0,0), saddle points at (1,!2) and (!1,!2).
  2. Saddle points at (0,0), (0,1) and (!2,0); local min at (!b ,a).
  3. Saddle point at (0,0), local max at (!2,!1) and at (8,4).
  4. Local mins at (1,!3) and (!1,3).