Mean+Value+Theorem

For any function that is continuous over the closed interval [a,b] and differentiable over the open interval (a,b), there exists a point c where the slope at that point equals the average rate of change from (a,b). This is written as: f'(c)= [f(b)-f(a)]/(b-a)

Ex: On the continuous interval [2,4], f(x)= x^2 This means there exists a point c where the slope at that point equals the average rate of change from 2 to 4. f'(c)= [f(4)-f(2)]/(4-2) = (8-4)/2            = 2