\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f\) and \(g\) be two convex functions on an interval \(I\). Show that the function \(h := \max(f, g)\), defined by \(h(x) = \max\bigl(f(x), g(x)\bigr)\), is convex on \(I\).
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