Answer:
Sometimes true.
Step-by-step explanation:
Let's grab the easiest cubic [tex]y=x^3[/tex]
It is easy to spot that it's always growing over its domain.
For the statement to be true the cubic need to be in the form
[tex]y= \frac 13 ax^3 +\frac12bx^2+cx + d[/tex] and [tex]a>0[/tex] and [tex]b^2-4ac >0[/tex]
Proof is trivial and it's left as an exercise to the reader. No, I'm joking. A cubic function has a quadratic derivative. You know that the sign of the first derivative determine the increase/decrease of the function, depending on sign. In order to be split the way you want it has to have two separate root and a positive leading coefficient.
