Definition: A point $\m \in \real^d$ is a strict local maximum of a function $f: \real^d \to \real$ if there exists a neighborhood $N_r(\m)$ such that $f(\m) > f(\x)$ for all $\x \in N_r(\m)$ with $\x \ne \m$.
Definition: A point $\m \in \real^d$ is a strict local maximum of a function $f: \real^d \to \real$ if there exists a neighborhood $N_r(\m)$ such that $f(\m) > f(\x)$ for all $\x \in N_r(\m)$ with $\x \ne \m$.