Review question

# 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

Ref: R9484

## Question

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