Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial derivatives of f. (b) Compute the two stationary points of f. Use the second derivative test to decide if each of them is a local maximum, minimum, or saddle point.

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.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Let
1
f(x,y) = x³ − x² − 8x + 2xy — 1⁄2y².
-
(a) Compute all first order and second order partial derivatives of f.
(b) Compute the two stationary points of f. Use the second derivative test to
decide if each of them is a local maximum, minimum, or saddle point.
Transcribed Image Text:Let 1 f(x,y) = x³ − x² − 8x + 2xy — 1⁄2y². - (a) Compute all first order and second order partial derivatives of f. (b) Compute the two stationary points of f. Use the second derivative test to decide if each of them is a local maximum, minimum, or saddle point.
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9780321964038
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