Checking the Mean Value TheoremThe function is zero at x =

Chapter 4, Problem 15E

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QUESTION:

Problem 15E

Checking the Mean Value Theorem

The function is zero at x = 0 1and x = 1 and differentiable on (0, 1), but its derivative on (0, 1) is never zero. How can this be? Doesn’t Rolle’s Theorem say the derivative has to be zero somewhere in (0, 1)? Give reasons for your answer.

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QUESTION:

Problem 15E

Checking the Mean Value Theorem

The function is zero at x = 0 1and x = 1 and differentiable on (0, 1), but its derivative on (0, 1) is never zero. How can this be? Doesn’t Rolle’s Theorem say the derivative has to be zero somewhere in (0, 1)? Give reasons for your answer.

ANSWER:

Problem 15E

Checking the Mean Value Theorem

The function is zero at x= 0 1and x = 1 and differentiable on (0, 1), but its derivative on (0, 1) is never zero. How can this be? Doesn’t Rolle’s Theorem say the derivative has to be zero somewhere in (0, 1)? Give reasons for your answer.

Step by step solution

Step 1 of 3

The given function is ,

The function show that it is not continuous over the interval.

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