Chapter 4.2, Problem 18E

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 11-26, determine whether Rolle's Theorem can be applied to f on the closed interval [a, b] If Rolle's Theorem can be applied, find all values of e in the open interval (a, b) such that f ' ( x ) = 0 . If Rolle's Theorem cannot be applied, explain why not. f ( x ) = x 2 − 4 x − 1 , ⌈ − 2 , 2 ⌉

To determine

Whether Rolle’s Theorem can be applied to f(x)=x24x1 on the closed interval [2,2] and if yes, then the values of c in the open interval (2,2) such that f(c)=0.

Explanation

The function f(x)=x2âˆ’4xâˆ’1 is not defined at x=1 as the denominator of the function becomes 0 at x=1. Also, x=1 falls in the interval [âˆ’2,2], therefore f(x)=

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