Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / 7 / b / Solution

This exponential function is positive everywhere, with $y(0)=1$, $y\to \infty$ as $x\to -\infty$ and $y\to 0$ as $x\to \infty$. Its derivatives areIt is strictly decreasing overall, with a horizontal stationary inflection point at $(0,1)$. A second, nonstationary inflection point occurs at $x=(2/3{)}^{1/3}$, where $y=e^{-2/3}$. The only horizontal asymptote is $y=0$ toward positive infinity; the graph is not symmetric about the vertical axis.