Question

How do you find the interval in which the function `f(x)=2x^3 + 3x^2+180x` is increasing or decreasing?

Answer 1

It is increasing on the whole real line. (On the interval `(-oo,oo)`.)

A differentiable function is increasing on any interval on which its derivative is positive.

For the function is question, `f'(x)=6x^2+6x+180`. This derivative is never 0 for real `x`.
(Use the quadratic formula to solve `x^2+x+30=0`. The solutions are imaginary.)
In fact, this derivative is always positive.

Therefore, `f` is always increasing. I.e, `f` is increasing on `(-oo,oo)`.