Lesson: The Mean Value Theorem
In this lesson, we will learn how to use the mean value theorem.
Sample Question Videos
Worksheet: The Mean Value Theorem • 4 Questions • 1 Video
Nader 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?
Mariam 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?
Consider the result: If is differentiable on an interval and , then , a constant, for all .
Which of the following statements says exactly the same thing as the constant function result?
If is differentiable on an interval and not constant, we get points with . How does this show that at some point ?
Consider the statement that if is a differentiable function on an interval and there, then is strictly increasing on .
Which of the following statements is equivalent to the above?
What does it mean for a function to not be strictly increasing on the interval ?
Using the equivalent statement to the main result, how can you use the mean value theorem to prove the equivalent statement?