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Sure.
My question is how to prove:
How to prove this?
Is there any suggestions? plz
Problem:
Let r:(a,b)->R^2 be a regular parametrized plane curve. Assume that there exists t0,a<t0<b,such that the distance |r(t)| from the origin to the trace of r will be a maximum at t0. Prove that the curvature k of r at t0 satisfies |k(t0)|>=1/|r(t0)|.
It's actually an exercise in the text "Differential Geometry of Curves and Surfaces" by Manfredo Do Carmo.
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