# 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?