Find the monotone interval and extremum of the cubic power of y = x minus three X

Find the monotone interval and extremum of the cubic power of y = x minus three X

y'=3x^2-3
When x > 1 or X

F (x) / X exists in the limit where x tends to 0, and is defined. It is proved that x = 0 is differentiable. How to prove it

The limit of F (x) / X exists and is defined when x tends to zero, that is, limf (x) / x = a (a is a constant)
So f (x) = 0
X tends to 0 Lim [f (x + 0) - f (0)] / x = Lim [f (x) - 0] / x = Lim f (x) / x = a
Then f (x) is differentiable

Prove limx → 3 (x-3) / x = 0 by using the definition of function limit
Prove limx → 3 (x-3) / x = 0 by using the definition of function limit

Proof: first of all, define │ x-3 │