Chapter 9.3, Problem 1CP

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Find the average rate of change of f ( x ) =   30   − x − x 2 over [1, 4].

To determine

To calculate: The average rate of change of f(x)=30xx2 over [1,4].

Explanation

Given Information:

The function is f(x)=30âˆ’xâˆ’x2 over [1,4].

Formula used:

The average rate of change of a function y=f(x) from x=a to x=b is defined by

AverageÂ rateÂ ofÂ change=f(b)âˆ’f(a)bâˆ’a

Calculation:

Consider the provided function,

f(x)=30âˆ’xâˆ’x2

For x=1, substitute 1 for x in the above function,

f(x)=30âˆ’xâˆ’x2f(1)=30âˆ’1âˆ’(1)2=29âˆ’1=28

For x=4, substitute 4 for x in the given function,

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