(a) Explanation Given information: The given function is, f ( x ) = 1 4 x 4 − 1 3 x 3 − x 2 Calculation: The derivative of the function is the slope of the tangent line. The derivative of given function is, f ′ ( x ) = d d x f ( x ) = d d x ( 1 4 x 4 − 1 3 x 3 − x 2 ) Use the rules of differentiation to find the derivative of given function. d d x ( 1 4 x 4 − 1 3 x 3 − x 2 ) = d d x 1 4 x 4 − d d x 1 3 x 3 − d d x x 2 ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = 1 4 d d x x 4 − 1 3 d d x x 3 − d d x x 2 ( d d x [ c f ( x ) ] = c d d x [ f ( x ) ] ) = 1 4 ( 4 x 4 − 1 ) − 1 3 ( 3 x 3 − 1 ) − 2 x 2 − 1 ( d d x ( x ) n = n x n − 1 ) = x 3 − x 2 − 2 x This implies f ′ ( x ) = x 3 − x 2 − 2 x (b) To determine The points on the graph of f where the slope of the tangent line is equal to 0. (c) To determine The points on the graph of f where the slope of the tangent line is equal to 10 x .

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 49E

(a)

To determine

The points on the graph of f where the slope of the tangent line is equal to −2x .

(b)

To determine

The points on the graph of f where the slope of the tangent line is equal to 0.

(c)

To determine

The points on the graph of f where the slope of the tangent line is equal to 10x .

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Chapter 3.1, Problem 48E

Chapter 3.1, Problem 50E

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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The points on the graph of f where the slope of the tangent line is equal to − 2 x .

Solution Summary: The author explains that the derivative of a function is the slope of the tangent line.

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The points on the graph of f where the slope of the tangent line is equal to −2x .

The points on the graph of f where the slope of the tangent line is equal to 0.

The points on the graph of f where the slope of the tangent line is equal to 10x .

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Chapter 3 Solutions