Question: Suppose that I is a nonempty, open interval and that f: I Rm is differentiable on I. If f(I) Br(0) for some fixed

Suppose that I is a nonempty, open interval and that f: I → Rm is differentiable on I. If f(I) ⊂ ϑBr(0) for some fixed r > 0, prove that f(t) is orthogonal to fʹ(t) for all t ∈ I.

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