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Algebra
Question

A rectangle has one corner in quadrant I on the gr...

A rectangle has one corner in quadrant I on the graph of 

\( y = 16 - x ^ { 2 } \) , another at the origin, a third on the positive 

\( y \) -axis, and the fourth on the positive \( x \) -axis. See the figure (top, right). (a) Express the area \( A \) of the rectangle as a function of \( x \) . (b) What is the domain of \( A \) ? (c) Graph \( A = A ( x ) \) . For what value of \( x \) is \( A \) largest? 

Answer

 

\(\left. \begin{array} { l } { \text { (a) } A ( x ) = x ( 16 - x ^ { 2 } ) } \\ { \text { (b) Domain: } \{ x | 0 < x < 4 \} } \\ { \text { (c) The area is largest when } x \approx 2.31 \text { . } } \end{array} \right.\)

Solution
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