a. Explanation Given: It is given in the question that the function is f ( x ) = x 3 Concept Used: In this we have to use the concept of limits and function. We must use the formula of d y d x = s l o p e . Calculation: Let f ( x ) = x 3 ⇒ f ' ( x ) = 3 x 2 ,here we have to put x = 0 , 1 / 2 , 1 , 2 , 3 and we get some particular values. f ' ( 0 ) = 0 ; f ' ( 1 / 2 ) = 0 b. To determine Find the values of f ' ( − 2 ) , f ' ( − 1 2 ) , f ' ( − 1 ) and f ' ( − 3 ) by using symmetry. c. To determine Draw the graph of f ' by using the values of part (a) and (b). d. To determine Calculate the formula of f ' ( x ) . e. To determine Show that the guess in part (c) is correct by using the definition of derivative.

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3.2, Problem 20E

To determine

Find the value of f'(0),f'(12),f'(1) , f'(2) and f'(3) by a graphing zoom device.

To determine

Find the values of f'(−2),f'(−12),f'(−1) and f'(−3) by using symmetry.

To determine

Draw the graph of f' by using the values of part (a) and (b).

To determine

Calculate the formula of f'(x) .

To determine

Show that the guess in part (c) is correct by using the definition of derivative.

Expert Solution & Answer

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - 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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

Find the value of f ' ( 0 ) , f ' ( 1 2 ) , f ' ( 1 ) , f ' ( 2 ) and f ' ( 3 ) by a graphing zoom device.

Concept explainers

Videos

Find the value of f'(0),f'(12),f'(1) , f'(2) and f'(3) by a graphing zoom device.

Find the values of f'(−2),f'(−12),f'(−1) and f'(−3) by using symmetry.

Draw the graph of f' by using the values of part (a) and (b).

Calculate the formula of f'(x) .

Show that the guess in part (c) is correct by using the definition of derivative.

Chapter 3 Solutions