(a) Explanation Given information: The function is f ( x ) = 2 x 3 − 3 x 2 − 16 x + 3 and slope of the tangent line is − 4 . Formula used: The formula to calculate the slope of the tangent is, m = d y d x (2) Calculation: As y = f ( x ) , thus, y = 2 x 3 − 3 x 2 − 16 x + 3 (1) Differentiate both sides of the equation (1) with respect to x . d y d x = 2 ( 3 x 2 ) − 3 ( 2 x ) − 16 d y d x = 6 x 2 − 6 x − 16 Substitute − 4 for m and 6 x 2 − 6 x − 16 for d y d x in equation (2) to calculate the points. 6 x 2 − 6 x − 16 = − 4 6 x 2 − 6 x − 16 + 4 = 0 6 x 2 − 6 x − 12 = 0 x 2 − x − 2 = 0 [ take 6 common from the whole term ] Factorize the above equation (b) To determine To find: The equations of the tangent lines of part (a).

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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 3, Problem 47RE

(a)

To determine

To find: The points on the graph of f.

(b)

To determine

To find: The equations of the tangent lines of part (a).

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Chapter 3, Problem 46RE

Chapter 3, Problem 49RE

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Chapter 3 Solutions

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

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The points on the graph of f .

Solution Summary: The author explains how to find the points on the graph of f.