Let $0<u \in C^{\infty}(M)$, with compact Riemannian manifold $M$, then i want to prove two following facts
(i) Since $M$ is compact, there exist $x_0 \in M$ such that $u(x_0) = \sup_{M} u$, then $\Delta u(x_0) \leq 0$
(ii) Since $M$ is compact, there exist $x_0 \in M$ such that $u(x_0) = \inf_{M} u$, then $\Delta u(x_0) \geq 0$
How one can prove this statement?