Hi can anyone help me out with how to find the stationary points of this functions:

y = x/x^2+1Thanks I am completely at a loss

Printable View

- May 28th 2009, 06:44 PMEmililypadCan someone help me with this function
Hi can anyone help me out with how to find the stationary points of this functions:

*y = x/x^2+1*Thanks I am completely at a loss

- May 28th 2009, 07:29 PMapcalculus
Is it $\displaystyle \frac{x}{x^2 + 1}$?

Find the first derivative using the quotient rule, then set it equal to zero.

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

(check to verify the work above)

... so the zeros occur where $\displaystyle 1 - x^2 = 0$, which means x = 1 or x = -1.

Good luck! - May 28th 2009, 09:59 PMEmililypad
Yes thats correct and thank you so much.