Let $\displaystyle R $ be the ring of all real valued continuous functions on the closed unit interval. If $\displaystyle M$ is a maximal ideal of $\displaystyle R$, prove that there exists a real number $\displaystyle \gamma, \ 0 \leq \gamma \leq 1$ such that $\displaystyle M=M_{\gamma}=\{ f(x) \in R \ | \ f(\gamma)=0\}$