(a) Explanation Given Information: The provided function is f ( x ) = x sin x and the specified interval is ( 0 , π ) . Graph: Consider the provided function: f ( x ) = x sin x The steps used to graph the function f ( x ) = x sin x and its first derivatives by using graphic calculator Ti-83 are as follows: Step 1: Press ON button and then press Y= button. Step 2: Then, enter the function f ( x ) = x sin x as Y 1 = X sin ( X ) . Step 3: After then, select Y 2 by clicking on down button ∨ . Step 4: Then, go to MATH and select nDeriv( or press 8. A new window appears as d d ( ) | = . Step 5: Now select VARS and press right arrow key > to select “function”, once function is selected, select function Y 1 (b) To determine To calculate: The critical points of the trigonometric function f ( x ) = x sin x over the interval ( 0 , π ) . (c) To determine The interval over which the derivative of the trigonometric function f ( x ) = x sin x is increasing and decreasing over the interval ( 0 , π ) . (d) To determine The relative extremes of the function f ( x ) = x sin x 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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Chapter 8.4, Problem 78E

(a)

To determine

To graph: The function f(x)=xsinx and its first derivatives by using graphic calculator over the interval (0,π).

(b)

To determine

To calculate: The critical points of the trigonometric function f(x)=xsinx over the interval (0,π).

(c)

To determine

The interval over which the derivative of the trigonometric function f(x)=xsinx is increasing and decreasing over the interval (0,π).

(d)

To determine

The relative extremes of the function f(x)=xsinx in the interval (0,π).

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Chapter 8.4, Problem 77E

Chapter 8.4, Problem 79E

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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 ) = x sin x and its first derivatives by using graphic calculator over the interval ( 0 , π ) .

Solution Summary: The author explains the steps used to graph the function f(x)=x-mathrmsinx and its first derivatives using graphic calculator Ti-83.

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To graph: The function f(x)=xsinx and its first derivatives by using graphic calculator over the interval (0,π).

To calculate: The critical points of the trigonometric function f(x)=xsinx over the interval (0,π).

The interval over which the derivative of the trigonometric function f(x)=xsinx is increasing and decreasing over the interval (0,π).

The relative extremes of the function f(x)=xsinx in the interval (0,π).

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Chapter 8 Solutions