# Thread: Increasing interval and decreasing interval

1. ## Increasing interval and decreasing interval

I have got a complex function y=(x^2-4*x-1)/(2*x+1) and I have to show the increasing and decreasing intervals.
How to show it when y'=(2*x^2+2*x-2)/(2*x+1)^2 but I am not able to find zero points and therefore it is impossible to find the increasing and decreasing intervals.

2. Originally Posted by totalnewbie
I have got a complex function y=(x^2-4*x-1)/(2*x+1) and I have to show the increasing and decreasing intervals.
How to show it when y'=(2*x^2+2*x-2)/(2*x+1)^2 but I am not able to find zero points and therefore it is impossible to find the increasing and decreasing intervals.
Sketch the curve:

3. This is not precise answer.

4. The function,
$y=\frac{x^2-4x-1}{2x+1},x\not =-1/2$ then,
$y'=\frac{2x^2+2x-2}{(2x+1)^2},x\not =-1/2$.
By Fermat's Principle the necessary conditions is when the derivative is zero or does not exits. Notice it does not exist at $x=-1/2$ but the function itself does not posses that domain. Thus, $y'=0$. That happens when $2x^2+2x-2=0$,
Thus,
$x^2+x-1=0$
$x=\frac{-1\pm\sqrt{5}}{2}$.
Now you can use derivative test to determine whether they are maximum or minimum or neither.

5. Originally Posted by totalnewbie