   Chapter 9.3, Problem 6E ### 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

# Given f ( x ) =   x 2 +   3 x   +   7 , find the average rate of change of f(x) over each of the following pairs of intervals.(a) [1.9, 2] and [1.99, 2](b) [2, 2.1] and [2, 2.01](c) What do the calculations in parts (a) and (b) suggest the instantaneous rate of change of f(x) at x = 2 might be?

(a)

To determine

To calculate: The average rate of change of function f(x) if f(x)=x2+3x+7 over the intervals [1.9,2] and [1.99,2].

Explanation

Given Information:

The function f(x) is,

f(x)=x2+3x+7

Over the intervals [1.9,2] and [1.99,2].

Formula used:

If a function f(x) is defined in the interval [a,b], then its average rate of change is given by the formula,

Average rate of change=f(b)f(a)ba

Calculation:

Consider the function f(x),

f(x)=x2+3x+7

For the interval [1.9,2],

Substitute the values of x=1.9 in f(x) to get,

f(1.9)=(1.9)2+3(1.9)+7=3.61+5.7+7=16.31

Substitute the values of x=2 in f(x) to get,

f(2)=(2)2+3(2)+7=4+6+7=17

The average rate of change R of the function, f(x)=x2+3x+7 over the interval [1

(b)

To determine

To calculate: The average rate of change of function f(x) if f(x)=x2+3x+7 over the intervals [2,2.1] and [2,2.01].

(c)

To determine

The instantaneous rate of change of f(x) where f(x)=x2+3x+7 at x=2 based on average rate of change on the intervals [2,2.1], [2,2.01], [1.9,2] and [1.99,2].

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