Non-differentiable Function

Question

Compute the expression $\frac{f(x,y)-f(0,0)-∇f(0,0)•(x,y)}{||(x,y)-(0,0)||}$, for f$(x,y)=(2x^3+3y^3)^{1/3}$.

How do you find $∇f(0,0)$?? Isn't this undefined?

Answer 1

$\nabla f(0,0)(e_{1})=\dfrac{\partial f}{\partial x}(0,0)$ and $\nabla f(0,0)(e_{2})=\dfrac{\partial f}{\partial y}(0,0)$ if they exist.