Let f(x, y)=3x²y-2y² − 3x² -8y +2 i. Find the stationary points off ii. For each stationary point P found in (i), determine whether f has a local maximum, a local minimum, or a saddle point at P.

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.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 7CR
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7.
a.
Let f(x,y)=3x²y-2y²
− 3x² −8y+2
i. Find the stationary points of f
ii. For each stationary point P found in (i), determine whether ƒ has a local maximum, a
local minimum, or a saddle point at P.
b. Determine the maximum value of f(x, y, z)=xyz subject to the constraint
x² +9y² + 4z² = 36
Transcribed Image Text:7. a. Let f(x,y)=3x²y-2y² − 3x² −8y+2 i. Find the stationary points of f ii. For each stationary point P found in (i), determine whether ƒ has a local maximum, a local minimum, or a saddle point at P. b. Determine the maximum value of f(x, y, z)=xyz subject to the constraint x² +9y² + 4z² = 36
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