(a) you should know that extrema occur at critical values of x where f'(x) changes sign.

(b) you have more than enough info to sketch the graph.

(c) use the FTC to find g'(x), then look for x-values where g'(x) changes sign ... (+) to (-) , a relative max ... (-) to (+) , a relative min.

(d) points of inflection occur where g''(x) changes sign.