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Register a new userThe Integral of Second-order Directional Derivative
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Authors
Pisheng Ding
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Given a two-variable function f without critical points and a compact region R bounded by two level curves of f, this note proves that the integral over R of fs second-order directional derivative in the tangential directions of the interceding level curves is proportional to the rise in f-value over R. Also discussed are variations on this result when critical points are present or R becomes unbounded.
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