1. [0.5/5 Points] DETAILS PREVIOUS ANSWERS This problem illustrates the First Derivative Test. Suppose you compute a derivative of a continuous function g and simplify it as the following: 9'(x) = 30x (9x - 1) 9 - X (a) Find the critical points of g. X = 0 (smallest) X = X= (largest) (b) Determine the sign of g ' on each subinterval of the real number line where cp1, cp2, and cp3 refer to the critical points from smallest to largest. --Select--- + ---Select--- + ---Select--- + ---Select--- + cp 1 cp2 cp3 (c) Use the signs to classify each critical point as a local maximum, local minimum, or neither. cp1 ---Select-- cp2 ---Select-- cp3 ---Select--. 2. [3.5/5.5 Points] DETAILS PREVIOUS ANSWERS This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x ) + 4. 2x (a) Find f'(x) 1 + x (b) Find the critical point of f(x) . x = 0 2(1 - 3x 4) (c) Find f" (x) = ( 1 + x 4) 2 (d) Use the Second Derivative Test to classify the critical point of f. F"(c.p.) = 0.76 x . This means that fis (---Select-- at the critical point because f"(c.p.) is ---Select--- ;) We conclude that the critical point is ( ---Select--- of f