# Mean value theorem

### From Conservapedia

The **Mean value theorem** of Calculus states that for some value *c* on the function *f* on some interval [a, b], *f'(c)* (the slope of *f* at *c*) will equal the average slope over [a, b], provided that *f* is continuous over the interval [a, b] and differentiable on the interval (a, b).

This is written algebraically as: *f*(*b*) − *f*(*a*) = *f*'(*c*)(*b* − *a*), where c is between b and a.