# Lesson Worksheet: The Mean Value Theorem Mathematics • Higher Education

In this worksheet, we will practice interpreting and using the mean value theorem.

Q1:

Mason is not convinced that the mean value theorem is true because, he says, the function has the property that if we take and , we have , and yet there is no point where . What is his error?

• AThe function is not differentiable at . The theorem requires diferentiability on an interval.
• BThe theorem requires the domain to be an interval, which is not.
• CThe function is not continuous. The theorem requires continuity on an interval.
• DThe function should be strictly increasing on the interval.
• EThe function should be strictly decreasing on the interval.

Q2:

Madison is not convinced that the mean value theorem is true because, she says, the function is certainly differentiable on . But if we take and , we have , and yet there is no point where . What is her error?

• AThe function should be continuous on the interval.
• BThe theorem requires the domain to be an interval, which is not.
• CThe function should be strictly increasing on the interval.
• DThe theorem requires that the function be differentiable on its domain.
• EThe function should be strictly decreasing on the interval.

Q3:

Does the mean value theorem apply for the function over the interval ?

• AYes
• BNo

Q4:

Does the mean value theorem apply for the function over the interval ?

• ANo
• BYes

Q5:

Does the mean value theorem apply for the function over the interval ?

• AYes
• BNo

Q6:

Does the mean value theorem apply for the function over the interval ?

• AYes
• BNo

Q7:

Does the mean value theorem apply for the function over the interval ?

• ANo
• BYes

Q8:

Does the mean value theorem apply for the function over the interval ?

• AYes
• BNo

Q9:

For the function , find all the possible values of that satisfy the mean value theorem over the interval .

Q10:

For the function , find all the possible values of that satisfy the mean value theorem over the interval .

• A
• B
• C
• D0
• E

This lesson includes 11 additional questions for subscribers.