   Chapter 4.2, Problem 1E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The graph of a function f is shown. Verify that f satisfies the hypotheses of Rolle’s Theorem on the interval [0, 8]. Then estimate the value(s) of c that satisfy the conclusion of Rolle’s Theorem on that interval. To determine

To verify: Whether the function f(x) satisfies the conditions of Rolle’s Theorem on [0,8] ; estimate the value of c that satisfies the conclusion of Rolle’s Theorem on [0,8] .

Explanation

Rolle’s Theorem:

“Let a function f satisfies the following conditions,

1. A function f is continuous on the closed interval [a,b] .

2. A function f is differentiable on the open interval (a,b)

3. f(a)=f(b)

Then, there is a number c in an open interval (a,b) such that f(c)=0 .”

Verification:

The graph of the function f(x) is shown below in Figure 1.

From Figure 1, it is observed that the graph is continuous on the closed interval [a,b] as it has no breaks

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