Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2008 / Paper 1 / 17 / a / i

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- Solution i

Solution

The zero set consists of the three lines

x = 0

,

y = 0

and

y = x - 1

. Their pairwise intersections are

(0, 0), (1, 0), (0, - 1) .

The bounded triangle has

0 \leq x \leq 1

and

x - 1 \leq y \leq 0

. Its edges and interior contours are shown below.

Figure 1.
Negative contours inside the zero triangle, with outward boundary gradients and the interior minimum
. Details.

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