Recall that a (twice-differentiable) function f ( x ) {\displaystyle f(x)} is concave up (or convex) where f ″ ( x ) ≥ 0 {\displaystyle f''(x)\geq 0} and concave down (or concave) where f ″ ( x ) ≤ 0. {\displaystyle f''(x)\leq 0.}
