Sketch a qualitatively accurate picture of the graph find

Question

Let f(x) = x³ - 3 a²x 4 + a³

where a is some positive constant.

a. Find f(0), f( - 2a), f(a), f(2a). Then argue that the function has 3 roots.

b. Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing. Your answer will depend on a. (Hint: Treat a as a constant when you differentiate. For instance, the derivative of -3a²x is -3a².)

c. Find the intervals where f(x) is concave up and where it is concave down.

d. Sketch a qualitatively accurate picture of the graph.