f(x)=x^3- 12x+8

Derivation:

f'(x)=3x^2- 12

f''(x)=6x

Solution f' (x) = 3x 2- 12 = 0:

x 1=-2，x2=2

X & lt-2 or x>2, f' (x) >; 0, f(x) increases monotonically.

The monotone increasing interval is (-∞, -2) and.

The maximum point x=-2 and the minimum point x=2.