   Chapter 4.2, Problem 31E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

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 ) = 2 x + ( x 2 − 4 x ) ( 2 x / 4 ) , ⌈ 0 , 4 ⌉

To determine
Whether Rolle’s Theorem can be applied to f(x)=2+(x24x)(2x/4),[0,4] on the closed interval [a,b], values of c in the open interval (a,b) and graph the function.

Explanation

Rolle’s Theorem can be applied because the function is continuous and differentiable.

Rolle’s Theorem is,

f'(c)=0

Differentiating the function,

f'(x)=2x/4+1x2x/4+2ln2

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