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Let f1, f2, f3: [a,b] -->R be nonnegative concave functions such that f1(a) = f2(a) =...

Let f1, f2, f3: [a,b] -->R be nonnegative concave functions such that f1(a) = f2(a) = f3(a) = f1(b) = f2(b) = f3(b) = 0. Suppose that max(f1) <= max(f2) <= max(f3).

Prove that: max(f1) + max(f2) <= max(f1+f2+f3)

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