Mean value theorem

The  exercise appears under the Differential calculus Math Mission. This exercise explores the mean value theorem from calculus.

Types of Problems
There are three types of problems in this exercise:


 * 1) How many points satisfy the MVT: This problem presents a function. The student is asked to determine how many points in the interval would satisfy the Mean Value Theorem.Mvt1.png
 * 2) Select a bound on the value of the function: This problem presents some information about the derivative and a function. The student is asked to use the provided information to find a bound on the value of a value for the function.Mvt2.png
 * 3) Given the information, find the desired value: This problem provides a situation that provides an equation. The student is expected to use the provided information to find the value of the variable.Mvt3.png

Strategies
Knowledge of the mean value theorem and it's graphical representation are encouraged to ensure success on this exercise.
 * 1) The Mean value theorem says that if a function is continuous and differentiable than the slope of the secant line over the interval is equal to the slope of the tangent line at some point in the interval.
 * 2) The Mean value theorem is the Most valuable theorem in calculus. The fundamental theorem falls out practically as a corollary to this theorem.

Real-life Applications

 * 1) Most of the problems in this subsection are applications in some sense, so the majority of the exercises are applications also.
 * 2) The MVT is the MVT of calculus.