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How can I derive the formula for the normal unit-vector to the curve of a function at a given point $p$?

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If curve is represented by $f(x,y)=0$, then $\nabla f_{(x_0,y_0)}$ is normal vector to curve at point $(x_0,y_0)$

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What's the name for that reflected $\Delta$? – saadtaame Mar 7 '13 at 19:29
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'nabla', it is. – Aang Mar 7 '13 at 19:34

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