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### What is the geometric meaning of third derivative of a function at a point? [closed]

What is the geometrical meaning of third derivative of a function at a point?
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### Rectifying texture from image

I have a camera matrix $P$ which defines a projective transformation $\mathbb{P}^3 \rightarrow \mathbb{P}^2$. In the former space there is a plane $[ x|\pi^Tx=0 ]$. The image of the plane under $P$ ...