Consider the function f R² → R defined by : f(x, y) = 2x³ + 6x² - 6xy - 3y²– 12y. (a) Find the Cartesian coordinates of the two critical points of f. (b) Use the Second Derivative Test to determine the nature of these critical points of f.

Consider the function f R² → R defined by : f(x, y) = 2x³ + 6x² - 6xy - 3y²– 12y. (a) Find the Cartesian coordinates of the two critical points of f. (b) Use the Second Derivative Test to determine the nature of these critical points of f.

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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Question

Consider the function f : R² → R defined by
f(x, y) = 2x³ + 6x² - 6xy - 3y² - 12y.
(a) Find the Cartesian coordinates of the two critical points of f.
(b) Use the Second Derivative Test to determine the nature of these critical points of f.

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