= Solution
In the positive quadrant, both components of the <gradient> are positive. Along $y=x$ the arrows point along $(1,1)$; near the horizontal axis they point mainly upwards, and near the vertical axis mainly rightwards. The <level sets> are the <hyperbolas> $xy=f/2$, including the coordinate axes for level zero. The <gradient> is <orthogonal> to each regular <level set> and points towards increasing values of $f$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2-2018-q12-gradient-contours.png]
{title=Gradient vectors and hyperbolic level sets of twice the coordinate product}
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