increasing function

**gracy** · January 17th 2007, 10:22 PM

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

**CaptainBlack** · January 17th 2007, 10:47 PM

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

Thread: increasing function

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