Let V be a Hilbert space. Let f(x) = ∥x∥ for x ∈ V. Using the...

Let V be a Hilbert space. Let f(x) = ∥x∥ for x ∈ V. Using the definition of Frechet differentiation, show that ∇f(x) = x for all x ̸= 0. Furthermore, show that f(x) is not Frechet differentiable at x = 0.

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Colby Messinger answered 2 years ago

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