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Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...

Let f, g : [a, b] ---> R continuous such that

(f(a) - g(a)) (f(b) - g(b)) < 0.

a) Show that sup{|f(x) - g(x)| : x ϵ [a, b]} is strictly positive and

achieved (is a maximum).

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