   Chapter 8.4, Problem 79E ### 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 ) = 2 x  sin  x               ( 0 , 2 π )

(a)

To determine

To graph: The function f(x)=2xsinx and its first derivatives by using graphic calculator over the interval (0,2π).

Explanation

Given Information:

The provided function is f(x)=2xsinx and the specified interval is (0,2π).

Graph:

Consider the provided function:

f(x)=2xsinx

The steps used to graph the function f(t)=t2sint 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)=2xsinx as Y1=2Xsin(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()|=

(b)

To determine

To calculate: The critical points of the trigonometric function f(x)=2xsinx over the interval (0,2π).

(c)

To determine

The interval over which the derivative of the trigonometric function f(x)=2xsinx is increasing and decreasing over the interval (0,2π).

(d)

To determine

The relative extremes of the function f(x)=2xsinx in the interval (0,2π).

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