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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

If y = f(x) and x changes from x1, to x2, write expressions for the following.

(a) The average rate of change of y with respect to x over the interval [x1, x2].

(b) The instantaneous rate of change of y with respect to x at x = x1.

(a)

To determine

To express: The average rate of change of y with respect to x over the interval [x1,x2]

Explanation

Result used:

The average rate of change of y with respect to x is

ΔyΔx=f(x0+Δx)f(x0)Δx

Calculation:

The average rate of change of y with respect to x is

ΔyΔx=f(x0+Δx)f(x0)Δx

Where [x0,x]=[x1,x2] and Δx=x2x1.

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

ΔyΔx=f<

(b)

To determine

To express: The instantaneous rate of change of y with respect to x at x=x1

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