Given a function f ( x, y) = x3 + y3 + 3x2 -18y2 + 81y + 5 The function has four critical points in which one of them is a saddle point at (0,3) . Find three other critical points for the function and classify them as a maximum, a minimum, or a saddle point.

Given a function f ( x, y) = x3 + y3 + 3x2 -18y2 + 81y + 5 The function has four critical points in which one of them is a saddle point at (0,3) . Find three other critical points for the function and classify them as a maximum, a minimum, or a 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.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 7CR

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Question

Given a function

f ( x, y) = x³ + y³ + 3x² -18y² + 81y + 5

The function has four critical points in which one of them is a saddle point at (0,3) . Find three other critical points for the function and classify them as a maximum, a minimum, or a saddle point.

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