Would this be the total change in the function at a given point? It seems like it would solve to a single number, and since the gradient vector gives the changes in the i,j, and k axes, then the norm would be the total change of all the axes added together. Am I right in thinking this?
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See https://math.stackexchange.com/questions/366227/understanding-directional-derivative-and-the-gradient, https://math.stackexchange.com/questions/1378226/why-does-nabla-fx-y-z-point-in-the-direction-of-greatest-increase-of-the, https://math.stackexchange.com/questions/223252/why-is-gradient-the-direction-of-steepest-ascent and many other similar questions. – Hans Lundmark Oct 17 '22 at 19:43
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What is the definition of total change? – Hermis14 Oct 17 '22 at 19:55
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Except of course the usual vector norm is not the absolute value on each axis "added together". – aschepler Oct 17 '22 at 19:56