   Chapter 2.8, Problem 33E

Chapter
Section
Textbook Problem

(a) If f(x) = x4 + 2x, find f'(x).(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'

(a)

To determine

To find: The derivative of the function f(x)=x4+2x.

Explanation

Given:

The function is f(x)=x4+2x.

Formula used:

The derivative of a function f , denoted by f(x), is

f(x)=limh0f(x+h)f(x)h (1)

Calculation:

Obtain the derivative of the function f(x).

Compute f(x) by using the equation (1),

f(x)=limh0f(x+h)f(x)h=limh0(x+h)4+2(x+h)(x4+2x)h

Expand the numerator,

f(x)=limh0(x4 + 4x3h + 6x2h2 +4x

(b)

To determine

To check: The answer to part (a) is reasonable by comparing the graphs of f and f.

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