AHSME 1993 Problem 26

Find the largest positive value attained by the function $f(x)=\sqrt{8x-x^2}-\sqrt{14x-x^2-48}$, $x$ a real number.

$\text{(A) } \sqrt{7}-1 \text{(B) } 3 \text{(C) } 2\sqrt{3} \text{(D) } 4 \text{(E) } \sqrt{55}-\sqrt{5}$