Use the derivative f'(x)=(x-1)(x+2)(x+4) to determine the local maxima and minima of f, as well as the intervals of increase and decrease. It also asks for a sketch of f... I think that I can handle that.
From the given derivative, we see we have the 3 critical numbers: $\displaystyle x=-4,-2,1$ so we have 4 intervals. Since the roots are all of odd multiplicity, we know the sign of the derivative will alternate across intervals (so we really only need to test one interval). Then, use the first derivative test to determine the nature of the extrema. Can you proceed?