   Chapter 3.1, Problem 31E

Chapter
Section
Textbook Problem

# Find the critical numbers of the function. f ( x ) = 2 x 3 − 3 x 2 − 36 x

To determine

To find:

The critical numbers of the given function.

Explanation

1) Concept:

Differentiate f(x) with respect to x, and then find the values of x where f'x=0 and f'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:

fx=2x3-3x2-36x

4) Calculation:

Differentiate f(x) with respect to x by using power rule of derivative.

f'x=6x2-6x-36

f'(x) exists for all x because it is a polynomial function

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