= Solution
The graph is nonnegative, tends to $+\infty$ as $x\downarrow0$ and as $x\to\infty$, and vanishes only at $x=1$. Its <derivative> is $2\log x/x$, negative before one and positive after one, so $(1,0)$ is the unique global <minimum>. The second <derivative> is $2(1-\log x)/x^2$: the graph is convex for $0<x<e$ and concave for $x>e$, with an <inflection point> at $(e,1)$. These features determine the sketch in the left panel.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1-elementary-graphs.png]
{title=The squared logarithm, the half-amplitude double-frequency sine, and the directed elliptical path}
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