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f(x, y, z, w) = a cosz+acosy+acosz+acos w+zy+yz+zw which is a function of four variables, and it has a critical point at x=y=z=w = 0 (this is obvious; you do not need to verify it). (A) Classify the critical point, assuming a = 0. (B) Classify the critical point, assuming a = 1/2. (C) Classify the critical point, assuming a = 1.

f(x, y, z, w) = a cosz+acosy+acosz+acos w+zy+yz+zw which is a function of four variables, and it has a critical point at x=y=z=w = 0 (this is obvious; you do not need to verify it). (A) Classify the critical point, assuming a = 0. (B) Classify the critical point, assuming a = 1/2. (C) Classify the critical point, assuming a = 1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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This problem is about the function f(x, y, z, w) = a cos x + a cosy + a cosz+acos w+ xy + yz+zw which is a function of four variables, and it has a critical point at x=y=z=w=0 (this is obvious; you do not need to verify it). (A) Classify the critical point, assuming a = 0. (B) Classify the critical point, assuming a = 1/2. (C) Classify the critical point, assuming a = 1. (D) Classify the critical point, assuming a = √2. (E) Classify the critical point, assuming a = 2. (F) Determine the values of a for which the second derivative test fails, at the given critcal point.
Transcribed Image Text:This problem is about the function f(x, y, z, w) = a cos x + a cosy + a cosz+acos w+ xy + yz+zw which is a function of four variables, and it has a critical point at x=y=z=w=0 (this is obvious; you do not need to verify it). (A) Classify the critical point, assuming a = 0. (B) Classify the critical point, assuming a = 1/2. (C) Classify the critical point, assuming a = 1. (D) Classify the critical point, assuming a = √2. (E) Classify the critical point, assuming a = 2. (F) Determine the values of a for which the second derivative test fails, at the given critcal point.
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