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Suppose that f(a) =f(b) and inf {f(x) :x∈[a, b]}< α <sup{f(x) :x∈[a, b]}.Prove that there exist...

Suppose that f(a) =f(b) and inf {f(x) :x∈[a, b]}< α <sup{f(x) :x∈[a, b]}.Prove that there exist c, d∈[a, b] with (c Not equal d) such that f(c) =α=f(d)

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