# Math Help - increasing function

1. ## increasing function

find all open intervals on which the function f(x)= x/ x^2 + x -2 is decreasing

2. Originally Posted by gracy
find all open intervals on which the function f(x)= x/ x^2 + x -2 is decreasing
Let:

$f(x)=\frac{x}{x^2+2-2}$,

then:

$f'(x)=-\frac{x^2+2}{(x^2+x-2)^2}$

which is always $<0$ where it is defined. It is undefined at the roots of $x^2+x-2$ which are $x=-2$ and $x=1$.

Also $f(x)$ is decreasing where $f'(x)<0$.

Therefore $f(x)$ is decreasing on $(-\infty,-2),\ (-2,1)$ and $(1,\infty)$

RonL