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This might be a bit of a silly question. Just looking at the definition of a gradient of a scalar field in wikipedia:

http://en.wikipedia.org/wiki/Gradient" [Broken]

So, the gradient points in the direction of the greatest increase in scalar field.

From the definition with the partial derivatives, it is not clear to me why that vector should point in the direction of greatest increase though. I understand how one computes the gradient but from that definition how can one conclude that this will point in the direction of greatest change?

Many thanks for any help you can give me.

Cheers,

Luc

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# Question about the gradient of a function

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