Calculus

According to Clairaut's theorem (Schwarz's theorem), the mixed partial derivatives $\frac{\partial^2 f}{\partial x \partial y}$ and $\frac{\partial^2 f}{\partial y \partial x}$ are equal provided that:

Options:

• (A) Both mixed partial derivatives are continuous
• (B) $f(x, y)$ is a polynomial
• (C) $f(x, y)$ is homogeneous
• (D) $\nabla f = 0$