Question

Is a cubic function always increasing?

Answer 1

Define a cubic function :

Let $f\left(x\right)$ be a cubic function.

$f\left(x\right)=a{x}^3+b{x}^2+cx+d$

The derivative of $f\left(x\right)$ may be used to determine whether $f\left(x\right)$ is increasing or decreasing at any intervals in its domain.

If $f\text{'}\left(x\right)>0$at each point in an interval $\mathrm{I}$, the function is increasing

If $f\text{'}\left(x\right)<0$ at each point in an interval $\mathrm{I}$, the function is decreasing.

Hence, it depends on the function whether it is increasing or decreasing.