   Chapter 8.4, Problem 77E ### 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 ) =  sin  x − 1 3 sin3 x + 1 5 sin5 x               ( 0 , π )

(a)

To determine

To graph: The function f(x)=sinx13sin3x+15sin5x and also graph its first and second derivatives by using graphic calculator.

Explanation

Given Information:

The provided function is,

f(x)=sinx13sin3x+15sin5x

Graph:

Consider the provided function:

Y1=f(x)=sinx13sin3x+15sin5x

Graph the function f(x)=sinx13sin3x+15sin5x 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 Y1=sin(x)(1/3)sin(3x)+(1/5)sin(5x).

Step 3: After then, select Y2 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)=sinx13sin3x+15sin5x over the interval (0,π).

(c)

To determine

The sign of the derivative of the trigonometric function f(x)=sinx13sin3x+15sin5x over the interval (0,π).

(d)

To determine

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

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