Note:-• Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.• Answer completely.• You will get up vote for sure. Consider the function f: R²R defined byf(x, y) = 2x³-12x² - 6xy+3y² + 24y.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.

If a real function of two variables is differentiable whose second partial derivatives exists and…

R defined by f(x, y) = 2x³-12x² - 6xy+3y² +24y. Consider the function f: R²- 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 c

R defined by f(x, y) = 2x³-12x² - 6xy+3y² +24y. Consider the function f: R²- 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 c

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

Note:- • Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. • Answer completely. • You will get up vote for sure.

Consider the function f: R²R defined by
f(x, y) = 2x³-12x² - 6xy+3y² + 24y.
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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Step 1: The double derivative test

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Step 2: Part [a] Critical Points

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