Hypotheses of the Theorems of Calc 1

Use the function

below to answer the following questions.

The Intermediate Value Theorem guarantees a solution to

in which of the following intervals?

The Mean Value Theorem guarantees a solution to

in which of the following intervals?

Give an interval over which the Extreme Value Theorem applies to

, but the Mean Value Theorem does not. Explain.

is defined and yet has no absolute maximum over the interval

. Explain why this fails to contradict the Extreme Value Theorem.

Some calculus classes and textbooks name another theorem called Rolle's Theorem, usually stated as follows: If

is continuous over

and differentiable over

and

, then there exists some

in

such that

. Rolle's Theorem is merely a special case of which of our theorems?

L'Hopital's Rule The Intermediate Value Theorem The Mean Value Theorem The Squeeze Theorem The Extreme Value Theorem

Information: Hypotheses of the Theorems of Calc 1