Geometric interpretation of partial derivatives

Question

Let us suppose that $f: \mathbb{R}^3 \to \mathbb{R}$ is a homogeneous function (i.e., $f(tx)=tf(x)$) such that its partial derivative $$ \frac{\partial^3 f}{\partial x \partial y \partial z} $$ is a nonnegative function. What is the geometric interpretation of this condition?