= Hermite-Hadamard inequality
{c}
{title2=$f((a+b)/2)\leq\frac1{b-a}\int_a^bf\leq\frac{f(a)+f(b)}2$}
For a <continuous> <convex function> on $[a,b]$, where $a<b$, its integral average lies between its midpoint value and the average of its endpoint values. For a <concave function> both <inequalities> reverse. The bound involving endpoints follows by comparison with the <affine function> joining them and <monotonicity of the Riemann integral>. The midpoint bound follows from the <Jensen inequality> on equal-weight midpoint tags and the <Riemann sum convergence theorem>.
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