Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 2 / 18 / e

The upper branch leaves the origin horizontally and curves upward, growing like $x^{5/2}$. The lower branch shares the horizontal tangent, rises to its small maximum at $x=16/25$, then crosses the axis at $x=1$ and falls toward $-\infty$. Its concavity changes at $x=64/225$, before the maximum. A separate zoom makes those nearby lower-branch features visible.