I need help with these problems.

(1) Find the critical numbers of the function f(2:) = 2563 32:2 36a". (2) Given the following derivative function, what are the critical numbers of f (:3)? 2335 :1: f'(I) = 1 (3) Find the global max and global min values of f(117) = a: + i on the interval [0.2, 4]. Section 4.3 (4) Suppose a ball is dropped from a height of 200 ft. Its position at time t is 3(t) = 16t2 + 200. (a) Determine how long it takes before the rock hits the ground. (b) Find the average velocity 1/an of the rock for when the rock is released and the rock hits the ground. (c) Find the time, t, guaranteed by the mean value theorem when the instantaneous velocity of the rock is Vavg. Section 4.4 (5) Consider the function f(a:) = 3:3 + gag 36:13 + 4. (a) Find the local maximum and minimum values. (b) Find where the function is increasing or decreasing. (c) Find the intervals of concavity and the inection points. (6) Find the local maximum and minimum values of f (3:) = 1 + 3332 217:3 using either the First Derivative Test or the Second Derivative test