Linear Algebra and Its Applications · Problem 6.1.12

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-minima-maxima-saddle-points

Problem

Decide whether

F = x^2 y^2 - 2x - 2y

has a minimum at the point

x = y = 1

(after showing that the first derivatives are zero at that point).