(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 r = 1. %3D (b) (i) State the Mean Value Theorem....

(a) Use the definition of the derivative of a function at a point to show that the function<br>f :R → R defined by f(x) = |x – 1| is not differentiable at r = 1.<br>%3D<br>(b) (i) State the Mean Value Theorem.<br>(ii) Let a E R with a > 0 and let f : R R be a continuous and differentiable function<br>such that f(0) = a and |f'(x)| < 1 for all x € R. Use the Mean Value Theorem to<br>show that |f(x)| < a+ |x| for all a E R.<br>

Extracted text: (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 r = 1. %3D (b) (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)| < 1="" for="" all="" x="" €="" r.="" use="" the="" mean="" value="" theorem="" to="" show="" that="" |f(x)|="">< a+="" |x|="" for="" all="" a="" e="">

Jun 05, 2022

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(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 r = 1. %3D (b) (i) State the Mean Value Theorem....

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