To determine Sketch the graph of the function. Calculate the coordinates of local extreme points, inflection points, and absolute extreme points. Explanation Given information: The function is y = ln ( cos x ) . Calculation: The domain of the function is ( − ∞ , ∞ ) . Provide the function as shown below. y = ln ( cos x ) (1) Differentiate equation (1) with respect to x . y ′ = 1 cos x ( − sin x ) = − sin x cos x = − tan x (2) Differentiate equation (2) with respect to x . y ″ = − sec 2 x = − 1 cos 2 x The critical points occurs at a point where y ′ = 0 . Sketch the graph of the function y = ln ( cos x ) as shown in Figure 1. Thus, the graph is concave down on ( − 5 π 2 , − 3 π 2 ) , ( − π 2 , π 2 ) , ( 3 π 2 , 5 π 2 ) and so on. The curve increases on ( − 5 π 2 , − 2 π ) , ( − π 2 , 0 ) , ( 3 π 2 , 2 π ) and so on. The curve decreases on ( − 2 π , − 3 π 2 ) , ( 0 , π 2 ) , ( 2 π , 5 π 2 ) . There are no points of inflection for the function. Calculate the local maximum as shown below. Substitute − 4 π for x in Equation (1). y = ln ( cos ( − 4 π ) ) = ln ( 1 ) = 0 Substitute − 2 π for x in Equation (1)

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 4.4, Problem 69E

To determine

Sketch the graph of the function.

Calculate the coordinates of local extreme points, inflection points, and absolute extreme points.

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Chapter 4.4, Problem 68E

Chapter 4.4, Problem 70E

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Chapter 4 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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