Find the stationary point(s) and point of inflexion of the curve
Determine the nature of the stationary point(s)
Differentiate with respect to x and see where f'(x) = 0. That gives you the stationary points.
Then differentiate again w.r.t. x and see whether f''(x) is + or - at those points where f'(x) = 0. That will tell you whether those points are (local) minima or maxima.
While you're about it, see where f''(x) = 0 and that gives you your point(s) of inflection.