Answer all questions with step by step explanations.

\fFor exercises 4 and 5, use the Second Derivative Test to find the local extrema for the given function. Show your analysis and justify your reasoning. 4. 8(x) =3x-x5+5 5. h(x) =x3+3x2-2 h'(x ) = 3 x8+6 x 0 = 3x(x+2 ) X= 0 X=-2 ~ahead h( x ) = 6*+6 h"(o) = 6 (0 ) +6 = 6 h" ( - 2 ) = 6 ( - 2) + 6 = -6 . P (x) has a maximum at X = - 2 b/c 's" (x)0. ( positive Daily Lessons and Assessments for AP* Calculus AB, A Complete Course Mark Sparks 2012 Page 333\fThe graph of f'(x), a polynomial function, is given. First, state what type of functions f (x) and f " (x) should be. Then, based on the graph of f'(x), sketch possible graphs of f (x) and f " (x). 8. 9 . f ( x ) f (x) f' ( x ) Cubic f' (x ) f ( x ) f ( x) Him &CO: POL f " (x ) f " (x )