Explanation Given information: The value of f ( t ) are given in the following table. Calculation: The given table is, We draw graph of the above table as follows, The term d y / d x represents the first order derivative i.e. slope of the graph. By the definition the term d y / d x = Change in y Change in x From the table it is clear that as the value of t increases, the value of f ( t ) decreases To determine (b) To estimate: f ' ( 2 ) and f ' ( 8 ) .

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 2.4, Problem 19P

To determine

(a)

To find:

Whether first derivative appears to be positive or negative for the given table, find for second derivative also and explain.

To determine

(b)

To estimate:

f'(2) and f'(8).

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Chapter 2.4, Problem 18P

Chapter 2.4, Problem 20P

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Chapter 2 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To find: Whether first derivative appears to be positive or negative for the given table, find for second derivative also and explain.

Solution Summary: The author explains that the first derivative is negative everywhere, while the second is also negative in the given interval.