1. Find all the critical numbers of the function (Justify Your Answer) (a) f(x) = 5VI -2 I > 2 212 + 3x - 14 1 52 (Hint: Also investigate the existence of the derivative at 1=2) (b) f(x) = x2 - 2lnx 2. Determine with justification, the absolute maximum and minimum of the function below in the associated interval. (a) f(x) = 4x3 - 12x2 + 9x - 1 [0, 1] (b ) 529/5 + f (x) = 1 25 -24/5 [-1, 1] 3. Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all the numbers(s) c that satisfies the conclusion of the Mean Value Theorem. (a) f(x) = e2z [0, 1] (b) f(x) = sinx [0, 7] 4. Use the I. V.T and Rolle's Theorem/M. V.T to prove that the equation below has a unique solution in the associated interval. (a) 147 + 8x - 2 =0 [0, 1] (b) -10 + 6.x + 2 =0 [-1, 0]