   Chapter 9.3, Problem 21E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For each function in Problems 19-22, approximate f'(a) in the following ways. Use  f ( a + h ) − f ( a ) h with  h = 0.0001. (b) Graph the function on a graphing calculator. Then zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. f ' ( 4 )   for  f ( x ) = ( 2 x − 1 ) 3

(a)

To determine

To calculate: The value of f(4) using f(a+h)f(a)h with h=0.0001, for the function, f(x)=(2x1)3.

Explanation

Given Information:

The provided function is f(x)=(2x1)3.

Formula used:

For a function f(x), the derivative of f(x) at any value of x is defined by,

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

Calculation:

Consider the provided function,

f(x)=(2x1)3

Apply the formula for derivative,

f(x)=f(x+h)f(x)h

For x=4 and h=0.0001,

f(4)=f(4+0.0001)f(4)0

(b)

To determine

To calculate: The slope of the straight line obtained when the graph of the function, f(x)=(2x1)3, is plotted and it is zoomed till the straight line is obtained.

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