> [!note] Theorem > > If the [[Derivative#Higher Derivatives|second derivative]] $f^{\prime\prime}$ of some [[Science/Math/Functions/Function|function]] $f$ is greater than 0 over an interval, then the graph of that function is [[Concavity|concave up]]; if it is less than 0 over an interval, then the graph is concave down; otherwise it has no concavity over that interval.