Use the definition of the derivative of a function at a point to show that the function f : R → R defined by f(x) = |x – 1| is not differentiable at x = 1. (i) State the Mean Value Theorem. (ii) Let a...

$Use the definition of the derivative of a function at a point to show that the function f : R → R defined by f(x) = |x – 1| is not differentiable at x = 1. (i) State the Mean Value Theorem. (ii) Let a e R with a > 0 and let f : R → R be a continuous and differentiable function such that f(0) = a and |f'(x)|I < 1 for all x E R. Use the Mean Value Theorem to show that |f(x)| <a+ \x| for all x E R. $

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Jun 05, 2022

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Use the definition of the derivative of a function at a point to show that the function f : R → R defined by f(x) = |x – 1| is not differentiable at x = 1. (i) State the Mean Value Theorem. (ii) Let a...

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