Find the stationary points of this function using the

Question

This question concerns the function f(x)=x³ +3x² -24x+40.

(a) Find the stationary points of this function.

(b) (i) Using the strategy to apply the First Derivative Test, classify the left-hand stationary point found in part (a).

(ii) Using the Second Derivative Test, classify the right-hand stationary point found in part (a).

(c) Find the y-coordinate of each of the stationary points on the graph of the function f (x), and also evaluate f (0).

(d) Hence draw a rough sketch of the graph of the function f(x).