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

It is increasing on the whole real line. (On the interval $\left(- \infty , \infty\right)$.)
For the function is question, $f ' \left(x\right) = 6 {x}^{2} + 6 x + 180$. This derivative is never 0 for real $x$.
(Use the quadratic formula to solve ${x}^{2} + x + 30 = 0$. The solutions are imaginary.)
Therefore, $f$ is always increasing. I.e, $f$ is increasing on $\left(- \infty , \infty\right)$.