# factoring/increasing decreasing functions

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• Jan 5th 2008, 04:35 PM
johntuan
factoring/increasing decreasing functions
I am in Increasing and Decreasing Functions.

I'm just wondering how to factor this. The original question was y=1/x^2+1, and taking the derrivative i was left with y'=-2x/(x^2+1)^2.

how do i factor the derrivative to get the x's?
• Jan 5th 2008, 04:39 PM
galactus
What do you mean?. You want to solve for x?. It's already factored.

Do you want to set to 0 and solve for x?. If so, about the only value x can have is 0.
• Jan 5th 2008, 04:53 PM
johntuan
yeah i want to set it to = zero, but its kind of confusing because its a fraction and im not used to that.
• Jan 5th 2008, 05:00 PM
galactus
Well, you can't have division by 0 so concentrate on the numerator.

You have $\displaystyle \frac{-2x}{(x^{2}+1)^{2}}=0$

So, $\displaystyle -2x=0$

Solve for x.

If you want to find inflection points, find y'', set to 0 and solve for x.

$\displaystyle y''=\frac{2(3x^{2}-1)}{(x^{2}+1)^{3}}$

To set this to 0 and solve, just solve $\displaystyle 2(3x^{2}-1)=0$