document.write( "Question 370483: A rectangular piece of cardboard is 13 inches long and 9 inches wide. From each corner a square piece is cut out, and then the flaps are turned up to form an open box. Determine the length of a side of the square pieces so that the volume of the box is as large as possible. \r
\n" ); document.write( "\n" ); document.write( "i got this:
\n" ); document.write( "V=(13-2h)(9-2h)(h)
\n" ); document.write( "but what do i do next? \n" ); document.write( "

Algebra.Com's Answer #264071 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "You then \r\n" );
document.write( "\r\n" );
document.write( "1. Multiply out the right side\r\n" );
document.write( "\r\n" );
document.write( "2. Find  \r\n" );
document.write( "\r\n" );
document.write( "3. Set  = 0.\r\n" );
document.write( "\r\n" );
document.write( "4. Show that it is a maximum. \r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "1.\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( "\r\n" );
document.write( "2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.\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( "\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( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "using the + we get h = 5.588760432\r\n" );
document.write( "using the - we get h = 1.744572901\r\n" );
document.write( "\r\n" );
document.write( "4.\r\n" );
document.write( "Using the 2nd derivative test.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substituting h = 5.588760432 gives a positive second derivative\r\n" );
document.write( "which means the graph is concave upward there and is a minimum. But\r\n" );
document.write( "we want a maximum.  [We could also tell that this could not be the\r\n" );
document.write( "answer because we would be cutting more than half of the shorter side\r\n" );
document.write( "and this would be impossible.)\r\n" );
document.write( "\r\n" );
document.write( "Substituting h = 1.744572901 gives a negative second derivative\r\n" );
document.write( "which means the graph is concave downward there and is a maximum.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the correct answer is  h = \r\n" );
document.write( "or h = 1.744572901. \r\n" );
document.write( "\r\n" );
document.write( "This will gives a box of approximately 91.43817871 cubic inches.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );