please solve part a only

X 3. (a) A function f(x) satisfies f'(x) = 2+ 13 . 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 8(t) 5+ dt = 12 for x > 1. 1 4 + +2 X Find g(8). (c) Let I(a, b) = [x (1 -x)' dx, where a 2 2 and b 2 2 are integers. Show that I(a, b) = a I(a - 1, b + 1 ) . b+1