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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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Well the gradient is defined as the vector of partial derivatives so that it will exist if and only if all the partials exist. A zero gradient is still a gradient (it's just the zero vector) and we sometimes say that the gradient vanishes in this case (note that vanish and does not exist are different things). A function can still be well defined at a point without the gradient existing, in fact a function can still be continuous without the gradient existing.

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    Yes, that would be one example. The absolute value function itself is another.2012-11-06