# How do you determine the intervals for which the function is increasing or decreasing given f(x)=-x^3-2x+1?

Sep 18, 2017

$f \left(x\right)$ is always decreasing function and in interval notation it is decreasing for $\left(- \infty , \infty\right)$

#### Explanation:

For the function $f \left(x\right) = - {x}^{3} - 2 x + 1$, as $x \to \infty$, $f \left(x\right) \to - \infty$ and as $x \to - \infty$, $f \left(x\right) \to \infty$

As $\frac{\mathrm{df}}{\mathrm{dx}} = f ' \left(x\right) = - 3 {x}^{2} - 2$ and as ${x}^{2}$ is always positive,

$f ' \left(x\right)$ is always negative and hence

$f \left(x\right)$ is always decreasing function and in interval notation it is decreasing for $\left(- \infty , \infty\right)$

graph{-x^3-2x+1 [-40, 40, -20, 20]}