Question: For any a > 0 prove that the function f(q) = qlog 2 q + (a-q)log 2 (a-q), q > 0 attains its minimum at

For any a > 0 prove that the function

f(q) = qlog2q + (a-q)log2(a-q), q > 0

attains its minimum at q = a/2.

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