This lesson includes 11 additional questions for subscribers.
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
Q7:
Does the mean value theorem apply for the function over the interval ?
- ANo
- BYes