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I need to prove that f(x) has a fixed point, given that f'(x) >= 2 for all x.

my problem is that I've reached the part in which g(x) = f(x) - x

and g'(x) = f'(x) - 1 and therefore g'(x) >= 1

but now i'm completely stuck. I knwo that I need to use the mean value theorem, but i just dont know where.

thanx.

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# Fixed Point of a function

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