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Today my lecturer wrote on the blackboard

[tex]

\max \left\{ {\alpha f(x) + (1 - \alpha )f(y)\,\,,\,\,\alpha g(x) + (1 - \alpha )g(y)} \right\}\,\,\,\, \le \,\,\,\alpha \max \left\{ {f(x)\,\,,\,\,g(x)} \right\} + (1 - \alpha )\max \left\{ {f(y)\,\,,\,\,g(y)} \right\},

[/tex]

where x, y are variables in allR, andalphais a constant in [0;1]. I must admit, I cannot quite see why this inequality holds. Are there some rules about themaximumthat is being used here?

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# Inequality and maximum

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