Can we sketch the curve $y=e^{-x}/(1+x^2)$?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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 \(x \to -\infty\), \(y \to \infty\).)