Let x(s) be a curve with arc length parametrization, and satisfies ∣∣x(s)∣∣≤∣∣x(s0)∣∣≤1 for all s sufficiently close to x0. Prove κ (s0) > 1. (Hint: Consider f(s) = ||x(s)|| 2 . Then f(s) has a local maximum at s0. Calculate f''(s0))
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