Find the monotone interval, extreme value of concave-convex interval and eight points of the function y = x 3-3x 2- 1

Take the derivative of y'=3x 3-3x 2- 1 and get y'=3x? -6x, so that y' = 3x? -6x=0

X 1=0 and x2=2 are obtained.

The inflection points are (0,-1) and (2, -5) respectively.

The convex interval is (-∞, 2), and the maximum value is-1.

The minimum value of convex interval is 0, +∞) is -5.