Chapter 4.3, Problem 17E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Intervals on Which a Function Is Increasing or Decreasing In Exercises 11-22, find the open intervals on which the function is increasing or decreasing. y = x − 2 cos x , 0 < x < 2 π

To determine

To calculate: The open intervals for which the provided function y=x2cosx,  0<x<2π is increasing or decreasing.

Explanation

Given:

The function y=xâˆ’2cosx,Â Â 0<x<2Ï€

Formula Used:

For any function g(x) that is differentiable in the interval (a,b) and continuous in the interval [a,b], the function g(x) can be classified as an increasing or a decreasing function based on the following conditions:

If d(g(x))dx>0 for the interval (a,b), the function g(x) is said to be increasing in the interval [a,b].

If d(g(x))dx<0 for the interval (a,b), the function g(x) is said to be decreasing in the interval [a,b].

Calculation:

Differentiate the provided function and equate it to zero to obtain the critical points:

dydx=1+2sinx1+2sinx=0sinx=âˆ’12x=7Ï€6,11Ï€6

These critical point gives three open intervals (0,7Ï€6),(7Ï€6,11Ï€6),(11Ï€6,2Ï€)

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