   Chapter 3.1, Problem 39E

Chapter
Section
Textbook Problem

# Find the critical numbers of the function. F ( x ) = x 4 / 5 ( x − 4 ) 2

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=x45x-42

4) Calculation:

By using the product rule of derivative,

F'x=x45ddxx-42+ddxx45x-42

By using the chain rule of derivative,

F'x=x452(x-4)+45x-15x-42

F'x=2x45x-4+4x-425x15

By simplifying,

F'x=2x45x-4·5x15+4x-425x1

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