Explanation Given: The functions f ( x ) = 4 x − 1 3 x 3 Formula used: The formula to find the average rate of change is A ( x ) = f ( x 2 ) − f ( x 1 ) x 2 − x 1 Calculations: The function is f ( x ) = 4 x − 1 3 x 3 a) For x = x 1 = 1.9 , we substitute the value of x as 1.9. For x = x 2 = 2.1 , we substitute the value of x as 2.1 . We get f ( x 1 ) = f ( 1.9 ) = 4 ( 1.9 ) − 1 3 1.9 3 = 5 .3136666666666667 f ( x 2 ) = f ( 2.1 ) = 4 ( 2.1 ) − 1 3 ( 2.1 ) 3 = 5 .313 Substituting the values in the formula for average rate of change, we get A ( x ) = f ( x 2 ) − f ( x 1 ) x 2 − x 1 = 5.313 − 5 .3136666666666667 2.1 − 1.9 = -0 .0006666666666667 0.2 = -0 .0033333333333335 b) For x = x 1 = 1.99 , we substitute the value of x as 1.99. For x = x 2 = 2.01 , we substitute the value of x as 2.01 . We get f ( x 1 ) = f ( 1.99 ) = 4 ( 1.99 ) − 1 3 1.99 3 = 5 .3331336666666667 f ( x 2 ) = f ( 2.01 ) = 4 ( 2.01 ) − 1 3 ( 2...

College Algebra with Modeling & Visualization (5th Edition)

5th Edition

ISBN: 9780321826138

Author: Gary K. Rockswold

Publisher: PEARSON

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Chapter 4.2, Problem 62E

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The average rate of change of $f$ on each interval. And determine what happens to this average rate of change as the interval decreases in length.

$\begin{array}{l} (a) [1.9, 2.1] \\ (b) [1.99, 2.01] \\ (c) [1.999, 2.001] \end{array}$

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Chapter 4.2, Problem 61E

Chapter 4.2, Problem 63E

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College Algebra with Modeling & Visualization (5th Edition)

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The average rate of change of f on each interval. And determine what happens to this average rate of change as the interval decreases in length. ( a ) [ 1.9 , 2.1 ] ( b ) [ 1.99 , 2.01 ] ( c ) [ 1.999 , 2.001 ]

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The average rate of change of f on each interval. And determine what happens to this average rate of change as the interval decreases in length. (a)[1.9, 2.1](b)[1.99, 2.01](c)[1.999, 2.001]

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Chapter 4 Solutions

The average rate of change of $f$ on each interval. And determine what happens to this average rate of change as the interval decreases in length.

$\begin{array}{l} (a) [1.9, 2.1] \\ (b) [1.99, 2.01] \\ (c) [1.999, 2.001] \end{array}$