Find the point of maxima and minima for the function f(x) = ∫t(t + 1)(t – 2) dt for t ∈ [0,x].
f'(x) = x(x + 1)(x – 2)
By the sign scheme, we can say that the function f(x) has points of minima at x = –1 and 2, and point of maxima at x = 0.
