Explanation Approach: For a function z = f ( x , y ) , let f x x , f y y , and f x y all exist in a circular region contained in the xy -plane with center ( a , b ) . Further, let f x ( a . b ) = 0 and f y ( a . b ) = 0 . After solving the above equation, we get the points that points are called the critical points. Calculation: Consider the given function: f ( x , y ) = 4 x 3 + 3 x y + 4 y 3 First find the critical points of each function: f x = ∂ ∂ x ( 4 x 3 + 3 x y + 4 y 3 ) = 12 x 2 + 3 y and, f y = ∂ ∂ y ( 4 x 3 + 3 x y + 4 y 3 ) = 3 x + 12 y 2 Equate to zero, we get:

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.3, Problem 1YT

To determine

To find:

The critical points for the given function.

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Chapter 9.2, Problem 69E

Chapter 9.3, Problem 2YT

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Chapter 9 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

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The critical points for the given function.

Solution Summary: The author explains how to find the critical points for a given function.

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To find: The critical points for the given function.

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Chapter 9 Solutions

To find:

The critical points for the given function.