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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

The average rate of change of f over [ 1 , 4 ] is

(A) always equal to

(B) never equal to

(C) sometimes equal to the average of its average rates of change over [ 1 , 2 ] , [ 2 , 3 ]  and  [ 3 , 4 ]

To determine

The correct option for the average rate of change of f over [1,4] out of the following options

A) always equal to

B) never equal to

C) sometimes equal to

The average of its average rates of change over [1,2], [2,3] and [3,4]

Explanation

Given information:

The options are:

A) always equal to

B) never equal to

C) sometimes equal to

When function is increasing or rising the slope of the function is positive and greatest where the curve is more slanted whereas when the function is decreasing or falling its slope is negative and it has the least value where the curve is the steepest.

The average rate of change of f over the interval [a,b] is defined by f(b)f(a)ba

Consider the interval [1,4],

Evaluate the average rate of change for the interval [1,4]

f(4)f(1)41=f(4)f(1)3

Consider the interval, [1,2]

Evaluate the average rate of change for the interval, [1,2]

f(2)f(1)21

Consider the interval, [2,3]

Evaluate the average rate of change for the interval [2,3]

f(3)f(2)32

Evaluate the average rate of change for the interval [3,4]

f(4)f(3)43

Add the rate of change of three intervals [1,2], [2,3] and [3,4]

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