Let f : [0, 1] -->R be a differentiable function with f(0) = f(1) = 0. Show that

Q: Let f : [0, 1] -->R be a differentiable function with f(0) = f(1) = 0. Show that

C[0,1] denotes the set of all continuous functions f:[0,1]->R. With the sup metric, it is a complete metric space. Let X be a subset of C[0,1] such that it contains only those functions for which f(0)=0 and f(1)=1 and f([0,1]) c [0,1]. X is a closed subset of C[0,1] hence it is complete. (X,sup) is a complete metric space. For every f:-X define f^ : [0,1] -> R by f^(x) = 3/4 * f(3x) for 0

ID: 2971969 • Letter: L

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Let f : [0, 1] -->R be a differentiable function with f(0) = f(1) = 0. Show that there exist a constant c such that integ. |f(x)| dx <= c* integ. |f '(x)| dx where x goes from 0 to 1

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C[0,1] denotes the set of all continuous functions f:[0,1]->R. With the sup metric, it is a complete metric space. Let X be a subset of C[0,1] such that it contains only those functions for which f(0)=0 and f(1)=1 and f([0,1]) c [0,1]. X is a closed subset of C[0,1] hence it is complete. (X,sup) is a complete metric space. For every f:-X define f^ : [0,1] -> R by f^(x) = 3/4 * f(3x) for 0

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Let f : [0, 1] -->R be a differentiable function with f(0) = f(1) = 0. Show that

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