A maximal ideal in a function ring

Let $C ([0, 1])$ be the (commutative) ring of continuous, real-valued functions on the unit interval, and let

M = {f \in C ([0, 1]) ∣ f (\frac{1}{2}) = 0} .

Prove that $M$ is a maximal ideal.

View

L A T E X

code

Let $\mathcal{C}([0,1])$ be the (commutative) ring of continuous, real-valued functions on the unit interval, and let
\[
	M=\left\{f\in \mathcal{C}([0,1])\,\mid\, f\left(\frac{1}{2}\right)=0\right\}.
\]
Prove that $M$ is a maximal ideal.