   Chapter 4.1, Problem 38E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the critical numbers of the function. g ( x ) = 4 − x 2 3

To determine

To find: The critical number of the function g(x)=4x23.

Explanation

Definition used:

A critical number of a function f is a number c, if it satisfies either of the below conditions:

(1) f(c)=0

(2) f(c) does not exist.

Formula used:

Chain Rule:

If two functions g(x) and h(x) are differentiable, then the derivative of f(x)=g(h(x)) is,

f(x)=g(h(x))(h(x)) (1)

Calculation:

Obtain the first derivative of the given function.

g(x)=ddx(4x2)13

Apply the chain rule as shown in equation (1).

g(x)=13(4x2)23(2x)=2x3(4x2)23

Set g(x)=0 and obtain the critical number

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