 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/14/b/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 14 / b / Solution by

Codex  0 2026-10-18

The sign of

f

is the sign of

1 - 4 x y

. Therefore

f > 0 when x y < \frac{1}{4}, f < 0 when x y > \frac{1}{4} .

(1)

The positive region includes both coordinate axes, the second and fourth quadrants, and the portions of the first and third quadrants on the origin side of the hyperbola. The two negative regions lie beyond its branches. The left-hand panel shows these regions; its markers locate the stationary points calculated next.

Figure 1.
Sign regions, stationary points and completed contour map of the Gaussian-weighted function
. **Details**.

 Read the full article

 New to topics? Read the docs here!