In Exercises 43 through 46, the first derivative f'(x) of a certain function f(x) is given. In each case,

(a) Find intervals on which f is increasing and decreasing.

(b) Find intervals on which the graph of f is concave up and concave down.

(c) Find the x coordinates of the relative extrema and inflection points of f.

(d) Sketch a possible graph for f(x)

f'(x) = x² − 2x − 8