3. (a) A function f(x) satises f'(x) = 233:3 . Let f(1) = 0. Use the Mean Value Theorem (MVT) to determine the range of possible values for f(2)- (b) Suppose g(t) is a continuous function satisfying 3\") _1_2 5+f4+t2dtx for x>1. Find g(8). 1 (c) Let I(a, b) = f x\" (1 x)" dx, where a 2 2 and b 2 2 are integers. Show that O :1 1(a, b) = I(a 1, b + 1). b+1