(a) Explanation Given Information: The provided function is, f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x Graph: Consider the provided function: Y 1 = f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x Graph the function f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x and also graph its first and second derivatives by using graphic calculator Ti-84. The steps used to graph the provided function and its first and second derivative by using graphic calculator Ti-84 are follow as: Step 1: Press ON button and then press Y= button. Step 2: Then, enter the function Y 1 = sin ( x ) − ( 1 / 3 ) sin ( 3x ) + ( 1 / 5 ) sin ( 5x ) . Step 3: After then, select Y 2 by clicking on down button ∨ . Step 4: Then, go to MATH and select nDeriv( or press 8) (b) To determine The critical points of the trigonometric function f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x over the interval ( 0 , π ) . (c) To determine The sign of the derivative of the trigonometric function f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x over the interval ( 0 , π ) . (d) To determine The relative extremes of the function in the interval ( 0 , π ) .

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 8.4, Problem 77E

(a)

To determine

To graph: The function f(x)=sinx−13sin3x+15sin5x and also graph its first and second derivatives by using graphic calculator.

(b)

To determine

The critical points of the trigonometric function f(x)=sinx−13sin3x+15sin5x over the interval (0,π).

(c)

To determine

The sign of the derivative of the trigonometric function f(x)=sinx−13sin3x+15sin5x over the interval (0,π).

(d)

To determine

The relative extremes of the function in the interval (0,π).

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Chapter 8.4, Problem 76E

Chapter 8.4, Problem 78E

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Chapter 8 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 1SWU Ch. 8.1 - Prob. 2SWU Ch. 8.1 - Prob. 3SWU Ch. 8.1 - Prob. 4SWU Ch. 8.1 - Prob. 5SWU Ch. 8.1 - Prob. 6SWU

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To graph: The function f ( x ) = sin x − 1 3 sin 3 x + 1 5 sin 5 x and also graph its first and second derivatives by using graphic calculator.

Solution Summary: The author explains the steps used to graph the provided function and its first and second derivatives by using graphic calculator Ti-84.

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Videos

To graph: The function f(x)=sinx−13sin3x+15sin5x and also graph its first and second derivatives by using graphic calculator.

The critical points of the trigonometric function f(x)=sinx−13sin3x+15sin5x over the interval (0,π).

The sign of the derivative of the trigonometric function f(x)=sinx−13sin3x+15sin5x over the interval (0,π).

The relative extremes of the function in the interval (0,π).

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Chapter 8 Solutions