A function is increasing where its first derivative is positive. Thus, we have to find the intervals where the first derivative of function is positive.

f(x)=x³-12x

f'(x)=3x²-12

So the function is increasing where f'(x)>0

Namely:

3x²-12>0

3x²>12

x²>4

This is possible when x>2 and when x<-2

Thus the function is increasing in the interval (-∞, -2)U(2,∞)