9. Differentiation

Mean Value Theorem — Quiz

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

Practice Questions

Question 1

Which pair of conditions must a function $f$ satisfy on $[a,b]$ to use the Mean Value Theorem?

Question 2

What does the Mean Value Theorem guarantee if its hypotheses are satisfied on $[a,b]$?

Question 3

For $f(x)=x^2$ on $[1,3]$, what value of $c$ does the Mean Value Theorem guarantee?

Question 4

Which theorem is the special case of the Mean Value Theorem when $f(a)=f(b)$?

Question 5

For $f(x)=\sin x$ on $[0,\pi]$, what value of $c$ does the Mean Value Theorem guarantee?