Reference no: EM131579609

Question: Suppose that a function satisfies the same conditions as in the previous exercise, except that f(a) f(b) One such function is illustrated in Figure. Show that if the figure is rotated so that the dotted line joining A(a, f(a)) to B(b, f(b)) is horizontal, then the rotated figure satisfies all the conditions of Rolle s Theorem. Therefore, there must be at least one point c, a

f'(c) = [f(b) - f(a)/(b - a)]

This result is known as the Mean Value Theorem, or The Law of the Mean.