# Given f'(x) = (x+1)(x-2)²g(x) where g is a continuous function and g(x) < 0 for all x. On what interval(s) is f decreasing?

Sep 28, 2016

$x > - 1$

#### Explanation:

For $f \left(x\right)$ to be decreasing is necessary that

$f ' \left(x\right) < 0$ so

$\left(x + 1\right) {\left(x - 2\right)}^{2} g \left(x\right) < 0$

If $g \left(x\right) < 0 \forall x \in \mathbb{R}$ then this is equivalent to

$\left(x + 1\right) {\left(x - 2\right)}^{2} > 0$

Here ${\left(x - 2\right)}^{2} \ge 0$ so the condition is

$x + 1 > 0$ or $x > - 1$