document.write( "Question 1084031: I need to solve the problem in this link please \r
\n" ); document.write( "\n" ); document.write( "https://drive.google.com/open?id=0B2SbxAb-ajtfRW00d2NCZWdFSW8
\n" ); document.write( "

Algebra.Com's Answer #698104 by ikleyn(52903)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "The length of the rectangle is 2x (from -x to +x). It is \"horizontal\" dimension.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The height of the rectangle is f(x) = \"8+-+2x%5E2\". It is \"vertical\" dimension.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area of the rectangle is  A(x) = \"2x%2A%288-2x%5E2%29\" = \"16x+-+4x%5E3\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find the maximum, take the derivative and equate it to zero:\r\n" );
document.write( "\r\n" );
document.write( "\"%28dA%28x%29%29%2F%28dx%29\" = 16 - 12x^2 = 0.\r\n" );
document.write( "\r\n" );
document.write( "====>  \"x%5E2\" = \"16%2F12\"  ====>  x = \"sqrt%2816%2F12%29\" = \"4%2F%282%2Asqrt%283%29%29\" = \"%282%2Asqrt%283%29%29%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You calculate maximal area A(x) by substituting x = \"%282%2Asqrt%283%29%29%2F3\".\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"graph%28+330%2C+330%2C+-2.5%2C+5.5%2C+-12.5%2C+15.5%2C%0D%0A++++++++++16x+-+4x%5E3%0D%0A%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plot A(x) = \"16x+-+4x%5E3\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );