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
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!