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1993 AMC 12 #26 - Maximum of a Function

Source:

January 3, 2012
functionalgebradomaininequalitiesconicsparabolacalculus

Problem Statement

Find the largest positive value attained by the function f(x)=8x−x2−14x−x2−48,x a real number f(x)=\sqrt{8x-x^2}-\sqrt{14x-x^2-48}, \qquad x\ \text{a real number} <spanclass=′latex−bold′>(A)</span> 7−1<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 23<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 55−5 <span class='latex-bold'>(A)</span>\ \sqrt{7}-1 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 2\sqrt{3} \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \sqrt{55}-\sqrt{5}
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