Average+Value+and+Mean+Value+Theorem+for+Integrals

Average Value Theorem: Let f(x) be a function that is continuous on the closed interval [a,b]. The average value of this function is defined at f(b)-f(a)/(b-a).

Mean Value Theorem: If y=f(x) is continuous at every point of the closed interval [a,b] and differentiable at every point of its interior (a,b), then there is at least one point c in (a,b) at which f '(c)= f(b)-f(a)/(b-a).