Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 13 / a / iii

The zero level set consists of the lines $x=1$ and $y=0$. The height is positive where $(x-1)y>0$ and negative where that product is negative. In each of the four resulting regions, closed nonzero contours surround its extremum; levels closer to zero extend further from the extremum towards the zero-level axes and towards large distance. The height tends to zero at infinity. The figure marks the four extrema and central saddle point, and includes the downhill path used below.