\(f(x)\) is a concave function over the interval I \( \Longleftrightarrow \) \(f^{''}(x)\leq 0,\ \forall x \in I\)

\(\)\(g(x)\) is a convex function over the interval I \( \Longleftrightarrow \) \(g''(x)\ge 0,\ \forall x \in I\)