Explanation Given information: Estimate the instantaneous rate of change of the function f ( x ) = x In x at x = 1 and x = 2. What do these values suggest about the concavity of the graph between 1 and 2? Calculation: The instantaneous rate of change at a point a is the derivative of f at a, written f ( a ), is defined as f ' ( a ) = lim h → 0 f ( a + h ) − f ( a ) h At a = 1, we estimate the derivative by putting a small value of h. for h = 0.001, f ' ( 1 ) ≈ lim h → 0 f ( 1.001 ) − f ( 1 ) 0.001 = lim h → 0 ( 1

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 2.1, Problem 38P

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Estimate the instantaneous rate of change of the function f ( x ) = x In x at x = 1 and x = 2. What do these values suggest about the concavity of the graph between 1 and 2?

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Chapter 2.1, Problem 37P

Chapter 2.1, Problem 39P

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Estimate the instantaneous rate of change of the function f ( x ) = x In x at x = 1 and x = 2. What do these values suggest about the concavity of the graph between 1 and 2?

Solution Summary: The author explains how to estimate the instantaneous rate of change of the function f ( x ) at a point of 1 and 2 by putting the value of h.

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Estimate the instantaneous rate of change of the function f ( x ) = x In x at x = 1 and x = 2. What do these values suggest about the concavity of the graph between 1 and 2?

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