   Chapter 3.2, Problem 2E

Chapter
Section
Textbook Problem

# Draw the graph of a function defined on [0, 8] such that f ( 0 ) = f ( 8 ) = 3 and the function does not satisfy the conclusion of Rolle’s Theorem on [0, 8].

To determine

To draw:

The graph of a function defined on [0, 8] such that f0=f8=3 and the function does not satisfy the conclusion of Rolle’s Theorem

Explanation

1) Concept:

Using the Rolle’s Theorem verify the result.

2) Theorem:

Rolle’s Theorem – Let f  be a function that satisfies the following 3 hypotheses:

i. f is continuous on the closed interval [a, b]

ii. f is differentiable on the open interval (a, b)

iii. f (a)=f (b)

Then there is a number c in (a, b) such that f'c=0

3) Given:

f0=f8=3

4) Calculation:

We have to construct a function which does not satisfy the conclusions of Rolle’s theorem

Therefore, from the conclusion

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