   Chapter 9.3, Problem 20E ### 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 ' ( − 1 )   for  f ( x ) = 2 x 3 − 11 x + 9

(a)

To determine

To calculate: The value of f(1) using f(a+h)f(a)h with h=0.0001, for the function, f(x)=2x311x+9.

Explanation

Given Information:

The provided function is f(x)=2x311x+9.

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)=2x311x+9

Apply the formula for derivative,

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

For x=1 and h=0.0001,

f(1)=f(1+0.0001)f(1)0.0001=f(0.9999)f(1)0

(b)

To determine

To calculate: The slope of the straight line obtained when the graph of the function, f(x)=2x311x+9, is plotted and it is zoomed till the straight line is obtained.

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