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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

For the function f graphed in Exercise 18:

(a) Estimate the value of f′(50).

(b) Is f'(10) > f'(30)?

(c) Is f ' ( 60 ) = f ( 80 ) f ( 40 ) 80 40 ? Explain.

(a)

To determine

To estimate: The value of f(50).

Explanation

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 value of f(50).

The function f(50) represents the rate of change of f with respect to t when t=50.

Consider the graph, the slope of the tangent line to the curve at x=50 passes through the points (43,f(43)) and (60,f(60)).

Note that, the rate of change of function f at t=a is equal to the slope of the tangent line to the function at the point t=a.

The average rate of change of function f at t=a is approximately equal to the rate of change of function f at t=a

(b)

To determine

To check: The statement f(10)>f(30) is valid or not.

(c)

To determine

To check: The statement f(60)>f(80)f(40)8040 is valid or not.

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