f(x, y) = (x² − 49)² – (y² – 9)² - A) f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum; f(7,0) = -81, local minimum; f(-7, 0) = -81, local minimum B) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum; f(7,0) = -81, local minimum; f(7,3)=0, saddle point; f(7,-3) = 0, saddle point; f(-7,0) = -81, local minimum; f(-7, 3) = 0, saddle point; f(-7, -3)=0, saddle point C) f(0, 0) = 2320, saddle point; f(7,3)=0, saddle point; f(7, -3) = 0, saddle point; f(-7,3)= 0, saddle point; f(-7, -3) = 0, saddle point D) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(7,0) = -81, local minimum
f(x, y) = (x² − 49)² – (y² – 9)² - A) f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum; f(7,0) = -81, local minimum; f(-7, 0) = -81, local minimum B) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum; f(7,0) = -81, local minimum; f(7,3)=0, saddle point; f(7,-3) = 0, saddle point; f(-7,0) = -81, local minimum; f(-7, 3) = 0, saddle point; f(-7, -3)=0, saddle point C) f(0, 0) = 2320, saddle point; f(7,3)=0, saddle point; f(7, -3) = 0, saddle point; f(-7,3)= 0, saddle point; f(-7, -3) = 0, saddle point D) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(7,0) = -81, local minimum
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
Find all local extreme values of the given function and identify each as a
Transcribed Image Text:5) f(x, y) = (x² − 49)² – (y2 - 9)²
A) f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum; f(7,0) = -81, local
minimum; f(-7, 0) = -81, local minimum
B) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local
maximum; f(7,0) = -81, local minimum; f(7, 3) = 0, saddle point; f(7, -3) = 0, saddle
point; f(-7, 0) = -81, local minimum; f(-7, 3) = 0, saddle point; f(-7, -3)=0, saddle
point
C) f(0, 0) = 2320, saddle point; f(7,3)=0,
f(-7, 3) = 0, saddle point; f(-7, -3)=0, saddle point
D) f(0, 0) = 2320, saddle point; f(0, 3) = 2401, local maximum; f(7,0) = -81, local
minimum
saddle point; f(7, -3) = 0, saddle point;
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