document.write( "Question 310349: The base of a rectangle is on the x-axis and its two upper vertices are on the parabola y=16-x^2. of all such rectangles, what are the dimensions of the one with greatest area? \n" ); document.write( "

Algebra.Com's Answer #221899 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "I think you need to draw a graph to understand what is going on:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The base of the green rectangle is 2x, because\r\n" );
document.write( "the base extends from -x to +x on the x axis,\r\n" );
document.write( "and that is a distance of 2x.\r\n" );
document.write( "\r\n" );
document.write( "The height of the green rectangle is y, so\r\n" );
document.write( "\r\n" );
document.write( "The area of the green rectangle is\r\n" );
document.write( "\r\n" );
document.write( "Area = base * height or\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since y and x are related by the equation of the parabola,\r\n" );
document.write( "\r\n" );
document.write( "we can substitute  for \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Set \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the positive value\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using the second derivative test,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( ", which is negative when ,\r\n" );
document.write( "which proves that A is a maximum when .\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the base of the largest rectangle, \r\n" );
document.write( "and its height is.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );