Calculus

If $z = f(x, y)$ has continuous second partial derivatives, Clairaut's theorem guarantees that:

Options:

• (A) $\frac{\partial^2 z}{\partial x \partial y} = \frac{\partial^2 z}{\partial y \partial x}$
• (B) $\frac{\partial^2 z}{\partial x^2} = \frac{\partial^2 z}{\partial y^2}$
• (C) $\nabla^2 z = 0$
• (D) $z$ is a linear function