1. Each of the following functions has a critical point at (0,0). Show that the second derivative tes is inconclusive for all three functions. Then classify the point (0,0) as a local maximum, local minimum, or saddle point using a graph. f(x,y) = x+ + y4 • f{x, y) = 16 – x* – y+ • f{x, y) = x* - y*
1. Each of the following functions has a critical point at (0,0). Show that the second derivative tes is inconclusive for all three functions. Then classify the point (0,0) as a local maximum, local minimum, or saddle point using a graph. f(x,y) = x+ + y4 • f{x, y) = 16 – x* – y+ • f{x, y) = x* - y*
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please double check your answer. All this is a 1 question so answer the whole question.

Transcribed Image Text:1. Each of the following functions has a critical point at (0,0). Show that the second derivative test
is inconclusive for all three functions. Then classify the point (0,0) as a local maximum, local
minimum, or saddle point using a graph.
f(x, y) = x4 + y4
• f(x, y) = 16 – x* – y4
• f(x,y) = x+ – y4
Expert Solution

Trending now
This is a popular solution!
Step by step
Solved in 10 steps with 3 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

