   Chapter 8.4, Problem 78E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Analyzing a Function In Exercises 75-80, use a graphing utility to (a) graph f and f’ in the same viewing window over the specified interval, (b) find the critical numbers of f, (c) find the open interval(s) on which f' is positive and the open interval(s) on which f' is negative, and (d) find the relative extrema in the interval. Function Interval f ( x ) = x  sin  x               ( 0 , π )

(a)

To determine

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

Explanation

Given Information:

The provided function is f(x)=xsinx and the specified interval is (0,π).

Graph:

Consider the provided function:

f(x)=xsinx

The steps used to graph the function f(x)=xsinx 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)=xsinx as Y1=Xsin(X).

Step 3: After then, select Y2 by clicking on down button .

Step 4: Then, go to MATH and select nDeriv( or press 8. A new window appears as dd()|=.

Step 5: Now select VARS and press right arrow key > to select “function”, once function is selected, select function Y1

(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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