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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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
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