1998 Fermat Problem 25

For each value of x, f(x) is defined to be the minimum value of the three numbers 2x+2, \frac{1}{2}x+1 and -\frac{3}{4}x+7. What is the maximum value of f(x)?

\textbf{(A)}\ \frac{2}{3}\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ \frac{17}{5}\quad \textbf{(D)}\ \frac{62}{11}\quad \textbf{(E)}\ 7

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