Find the critical points of the function f(x, y) = x¹ + y² − 64xy Answer: Starting with the point with the smallest z value, use the Second Derivative Test to determine whether each critical point is P₁ A. test fails ● B. a saddle point OC. a local maximum O D. a local minimum P₂ ● A. a saddle point B. test fails O C. a local minimum ○ D. a local maximum P3 O A. a local minimum ● B. a saddle point OC. test fails O D. a local maximum
Find the critical points of the function f(x, y) = x¹ + y² − 64xy Answer: Starting with the point with the smallest z value, use the Second Derivative Test to determine whether each critical point is P₁ A. test fails ● B. a saddle point OC. a local maximum O D. a local minimum P₂ ● A. a saddle point B. test fails O C. a local minimum ○ D. a local maximum P3 O A. a local minimum ● B. a saddle point OC. test fails O D. a local maximum
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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Question
E Q21
Transcribed Image Text:Find the critical points of the function f(x, y) = x¹ + y² − 64xy
Answer:
Starting with the point with the smallest z value, use the Second Derivative Test to determine whether each critical point is
P₁
A. test fails
● B. a saddle point
OC. a local maximum
O D. a local minimum
P₂
● A. a saddle point
B. test fails
O C. a local minimum
○ D. a local maximum
P3
O A. a local minimum
● B. a saddle point
OC. test fails
O D. a local maximum
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