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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The graph of a function f is shown.

(a) Find the average rate of change of f on the interval [20, 60].

(b) Identify an interval on which the average rate of change of f is 0.

(c) Which interval gives a larger average rate of change, [40, 60] or [40, 70]?

(d) Compute f ( 40 ) f ( 10 ) 40 10 ; what does this value represent geometrically?

Chapter 2.7, Problem 18E, The graph of a function f is shown. (a) Find the average rate of change of f on the interval [20,

(a)

To determine

To find: The average rate of change of f on the interval [20,60].

Explanation

Given:

The graph of the function y=f(x).

From the given graph, it is observed that the domain of the function is on the interval [0,80] and the co-domain of the function is [0,1000].

Formula used:

The average rate of change of y with respect to x on the interval [x1,x2] is,

ΔyΔx=f(x2)f(x1)x2x1 (1)

Calculation:

Obtain the average rate of change of f on the interval [20,60]

(b)

To determine

To find: The interval when the average rate of change of the function f is zero.

(c)

To determine

To find: The correct interval gives a larger average rate of change.

(d)

To determine

To compute: The value of f(40)f(10)4010 and write the meaning of this value represent geometrically.

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