Calculus

For a two-variable function $f(x, y)$, let $r = f_{xx}, s = f_{xy}, t = f_{yy}$. A stationary point is a local minimum if:

Options:

• (A) $r t - s^2 > 0$ and $r > 0$
• (B) $r t - s^2 > 0$ and $r < 0$
• (C) $r t - s^2 < 0$
• (D) $r t - s^2 = 0$