Let () = ³+ 15/2 ( ² ) 18 1.

a) Find () and ().

b) Construct a first derivative sign chart to determine the intervals where () is increasing or decreasing. Increasing: _____________________________ Decreasing: _____________________________

c) Use the First Derivative Test to find all relative maxima and minima. Answer as coordinate pairs. Relative maxima: _____________________________ Relative minima: _____________________________

d) Construct a second derivative sign chart to find the intervals where () is concave up or down. Concave Up: _____________________________ Concave Down: _____________________________

e) Find the coordinates of the inflection point(s), if any. Answer as coordinate pairs.

f) Verify that the critical number(s) is/are extremum/extrema using the Second Derivative Test.

g) Make a rough sketch the graph of (), labeling all points found in the previous parts. Label your axes with a scale appropriate for the problem.