   Chapter 3.1, Problem 42E

Chapter
Section
Textbook Problem

# Find the critical numbers of the function. g ( x ) = 1 − x 2

To determine

To find:

The critical numbers of the given function

Explanation

1) Concept:

Differentiate g(x) with respect to x, and then find the values of x where g'x=0 and g'x doesn’t exist. That gives the critical numbers.

2) Definition:

A critical number of a function f   is a number c in the domain of f  such that either  f'c=0 or f'c does not exist.

3) Given:

gx=1-x2

4) Calculation:

g(x) can be written as gx=1-x212

Differentiate g(x) with respect to x by using the chain rule of derivative.

g'x=121-x212 - 1·ddx(1-x2)

g'x=121-x

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