At points where f'(x) = 0, these points are called the critical points, meaning that the function at those points are either relative minimums, relative maximums, or saddle points. So You got x = 2, 0 as the critical points. Now to determine if these critical points are local minimna or local max, you can apply the second derivative test.

if f''(2) < 0 then at the point x = 2, f is a relative maxima,

if f''(2) > 0 then at the point x = 2, f is a relative minima.

if f''(2) = 0, the test won't work and u need some other method of determining if relative max or min

Same for the point x = 0