Chapter 4, Problem 16RE

### 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 the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f ' ( c ) = f ( b ) − f ( a ) b − a If the Mean Value Theorem cannot be applied, explain why not. f ( x ) = 2 x − 3 x ,       [ − 1 , 1 ]

To determine

To calculate: The value of c such that f'(c)=f(b)f(a)ba with the help of Mean Value Theorem for f(x)=2x3x.

Explanation

Given:

The function f(x)=2xâˆ’3x in the interval [âˆ’1,1].

Formula used:

The Mean Value Theorem states that if a function g(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b) then for any câˆˆ(a,b),

gx

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