(1) Let the function $f(x)$ be defined as: for each $x \in \mathbf{R}, f(x)$ is the minimum value of the three numbers $x+2$, $4x+1$, and $-2x+4$. Then the maximum value of $f(x)$ is ( ).
(A) $\frac{1}{3}$
(B) $\frac{7}{3}$
(C) $\frac{8}{3}$
(D) 3
(1) In the same Cartesian coordinate system, draw the three lines $y=x+2$, $y=4x+1$, $y=-2x+4$ to see. Therefore, the answer is C.