(a) Explanation Given information: The given function is f ( x ) = x 3 + 1 . Formula used: (1) The sum or difference rule of differentiation is, d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] (2) If n is any real number then power rule of differentiation is, d d x ( x n ) = n x n − 1 Calculation: The slope of the tangent line of the graph of any function is equal to its derivative. Differentiate the given function with respect to x . f ′ ( x ) = d d x ( x 3 + 1 ) = d d x ( x 3 ) + d d x ( 1 ) ( Use sum rule ) = 3 x 3 − 1 + 0 ( Use power rule ) = 3 x 2 Substitute 12 for x to find the points where the slope of the tangent line is 12 (b) To determine The equations of the tangents lines that are obtained in part (a). (c) To determine To sketch: The graph of function f with two tangent lines.

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 3.1, Problem 47E

(a)

To determine

The points on the graph of f where slope of the tangent line is equal to 12.

(b)

To determine

The equations of the tangents lines that are obtained in part (a).

(c)

To determine

To sketch: The graph of function f with two tangent lines.

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Chapter 3.1, Problem 46E

Chapter 3.1, Problem 48E

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ 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

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AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - 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The points on the graph of f where slope of the tangent line is equal to 12.

Solution Summary: The author explains that the points on the graph of f where slope of the tangent line is equal to 12 are (-2,9).

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The points on the graph of f where slope of the tangent line is equal to 12.

The equations of the tangents lines that are obtained in part (a).

To sketch: The graph of function f with two tangent lines.

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Chapter 3 Solutions