 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/5/b/solution

H = (21 1 - 2), det H = - 5 < 0.

Its eigenvalues have opposite signs, so the stationary point is a saddle point. More directly, putting

x = 1 + u

and

y = - 1 + v

gives

f = u^{2} + uv - v^{2}

: it increases along

v = 0

and decreases along

u = 0

 New to topics? Read the docs here!