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 statement best describes the Mean Value Theorem for a function $f$ on an interval $[a,b]$?

Question 2

Which set of conditions is needed to apply the Mean Value Theorem to a function $f$ on $[a,b]$?

Question 3

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

Question 4

A function $f$ is continuous on $[2,6]$ and differentiable on $(2,6)$. If $f(2)=5$ and $f(6)=21$, what is the average rate of change of $f$ on $[2,6]$?

Question 5

If $f'(x)>0$ for every $x$ in $(a,b)$, what can be concluded about $f$ on $[a,b]$?