Chapter 13 - Partial Derivatives - 13.3 Partial Derivatives - Exercises Set 13.3 - Page 936: 16

$\frac{\partial f}{\partial x} < 0$, $\frac{\partial f}{\partial y} > 0$.

Step 1 Moving to the right from $(x_0, y_0)$ (fixed $x_0$ and $y_0$) decreases $f(x, y)$, so $\frac{\partial f}{\partial x} < 0$. Step 2 Moving up from $(x_0, y_0)$ (fixed $x_0$ and $y_0$) increases $f(x, y)$, so $\frac{\partial f}{\partial y} > 0$. Result $\frac{\partial f}{\partial x} < 0$, $\frac{\partial f}{\partial y} > 0$.