A function f is defined by f(x) = x^3 - 3x^2 + 1. i) Write down f'(x). ii) Hence find the co-ordinates of the stationary points of the curve y=f(x).

i) Using the power rule, f'(x) = 3x² - 6x ii) To find stationary points, set f'(x) to 0: 3x² - 6x = 0. 3x(x - 2) = 0. x = 0  or  x = 2 So the co-ordinates are (0,f(0)) = (0, 1), and (2,f(2)) = (2,-3).