If \(y=\dfrac{e^{-x}}{1+x^2}\), prove that (i) \(y\) is always positive, (ii) \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) is never positive.

Find the coordinates of the point where \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=0\), and sketch the graph of the function.

(It can be assume that as \(x \to -\infty\), \(y \to \infty\).)