5. Analytical Applications of Differentiation

Using The Mean Value Theorem — Quiz

Test your understanding of using the mean value theorem with 5 practice questions.

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Practice Questions

Question 1

Which set of conditions must a function satisfy to apply the Mean Value Theorem on $[a,b]$?

Question 2

If $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, what does the Mean Value Theorem guarantee?

Question 3

A function satisfies the hypotheses of the Mean Value Theorem on $[1,5]$ and has $f(1)=2$ and $f(5)=10$. What is the average rate of change of $f$ on the interval?

Question 4

Rolle's Theorem is a special case of the Mean Value Theorem when which condition is added?

Question 5

Which function does not satisfy the hypotheses of the Mean Value Theorem on $[-1,1]$?