This activity uses the graphing calculator to visually describe the meaning behind the mean value theorem.
In Part I students study a function that is both differentiable and continuous on a given interval.
In Part II students study a function that is continuous, but not differentiable on a given interval.
In Part III students study a function that is not differentiable or continuous at a point on a given interval.
From their conclusions students build understanding for when the conditions of the Mean Value Theorem are guaranteed.
This activity sheet also contains 8 application problems for the Mean Value Theorem. Students are presented functions in algebraic form, graphical form, and tabular form.
An Assignment for the Mean Value Theorem is also on sale in my story. Look for the title: Assignment for Mean Value Theorem".