# Mean-Value Theorem

The mean-value theorem states that if *f*(*x*) is differentiable on the open interval (*a*, *b*) and continuous on the closed interval [*a*, *b*], there is at least one point *c* in (*a*, *b*) such that (*a* - *b*) *f*(*c*) = *f*(*a*) - *f*(*b*).

Mean-value theorem is a college-level concept that would be first encountered in a Calculus I course. It is an Advanced Placement Calculus AB topic and is listed in the California State Standards for Calculus.

### Prerequisites

Derivative: | A derivative is the infinitesimal rate of change in a function with respect to one of its parameters. |