11th Edition

ISBN: 9780136845881

Author: Sullivan

Publisher: VST

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Textbook Question

Chapter 14, Problem 39RE

Instantaneous Rate of Change The following data represent the revenue R (in dollars) received from selling x wristwatches at Wilk’s Watch Shop.

Wristwatches, x Revenue , R 0 0 25 2340 40 3600 50 4375 90 6975 130 8775 160 9600 200 10000 220 9900 250 9375

Find the average rate of change of revenue from x = 25 to x = 130 wristwatches.

Find the average rate of change of revenue from x = 25 to x = 90 wristwatches.

Find the average rate of change of revenue from x = 25 to x = 50 wristwatches.

Using a graphing utility, find the quadratic function of best fit.

Using the function found in part (d), determine the instantaneous rate of change of revenue at x = 25 wristwatches.

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Chapter 14, Problem 38RE

Chapter 14, Problem 40RE

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

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Chapter 14 Solutions

EBK PEARSON ETEXT PRECALCULUS -- ACCESS

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

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Solution Summary: The author calculates the average rate of change of revenue R from x=25 to 130 wristwatches at Wilk Watch Shop.

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