# How do you determine the intervals for which the function is increasing or decreasing given f(x)=x^3+3x^2-9x?

##### 1 Answer
Jul 17, 2017

We differentiate the function to find an expression for its slope: $f ' \left(x\right) = 3 {x}^{2} + 6 x - 9$. The function is increasing when its slope (gradient) is positive $\left(f ' \left(x\right) > 0\right)$ and decreasing when its slope is negative $\left(f ' \left(x\right) < 0\right)$.