Chapter 4.2, Problem 29E

### 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

# Using Rolle's Theorem In Exercises 27-32, use a graphing utility to graph the function on the closed interval ⌊ a , b ⌋ .Determine whether Rolle's Theorem can be applied to f on the interval and, if so, find all values of f in the open interval (a. b)such that f ' ( x ) = 0 . f ( x ) = x 2 − sin π x 6 , ⌈ − 1 , 0 ⌉

To determine

To calculate: The values of c in the open interval (1, 0) such that f'(c)=0 on determining whether Rolle’s Theorem can be applied to the function f(x)=x2sinπx6 on the closed interval [1,0] and graph the function using graphing utility.

Explanation

Given: f(x)=x2âˆ’sinÏ€x6,[âˆ’1,0]

Formula used:

ddx(xn)=nxnâˆ’1

Calculation:

Rolleâ€™s Theorem can be applied because the function is continuous and differentiable.

Rolleâ€™s Theorem is,

f'(c)=0

Differentiating the function,

f'(<

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