# When does a gradient vector of a function not exist?

I have a question that gives me a 3d function and asks me to calculate the gradient vector of it. This part I understand. It then asks me to indicate the points at which it does not exist. When does a gradient vector not exist? Is it when it equals to zero? Or does it mean when the function DNE.

Thanks.

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One might define $\nabla f(x)$ to be the unique vector $g$ such that $f(x +h) =f(x) +g^T h +o(h)$ as $|h| \to 0$ (assuming such a $g$ exists). –  littleO Nov 6 '12 at 22:03