Let F be the ring of continuous functions from $R$ to $R$. Let $A =\{f \in F \; | \; f(0)=0\}$ Show that $A$ is maximal in R.
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?