document.write( "Question 1035913: If x + y is 19, then what is the max value of xy? \n" ); document.write( "
Algebra.Com's Answer #650528 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "Let V = the value of xy\r\n" );
document.write( "\r\n" );
document.write( "V = xy\r\n" );
document.write( "\r\n" );
document.write( "Since x + y = 19, \r\n" );
document.write( "          y = 19-x\r\n" );
document.write( "\r\n" );
document.write( "V = x(19-x)\r\n" );
document.write( "\r\n" );
document.write( "V = 19x - x²\r\n" );
document.write( "\r\n" );
document.write( "That's a quadratic equation like y = ax²+bx+c,\r\n" );
document.write( "because we can write it this way:\r\n" );
document.write( "\r\n" );
document.write( "V = -x² + 19x + 0\r\n" );
document.write( "\r\n" );
document.write( "Then you can use the vertex formula to find\r\n" );
document.write( "the maximum (peak) value, since it's one of\r\n" );
document.write( "those upside-down U curves, which has its\r\n" );
document.write( "maximum at the top (the vertex), which you\r\n" );
document.write( "can tell because the coefficient of x² is\r\n" );
document.write( "negative.\r\n" );
document.write( "\r\n" );
document.write( "[If you're in calculus, you just take the \r\n" );
document.write( "derivative dV/dx and set it equal to 0.  You get \r\n" );
document.write( "the same maximum (vertex) value the algebra \r\n" );
document.write( "way or the calculus way).\r\n" );
document.write( "\r\n" );
document.write( "You finish.  Or you can ask me to help you\r\n" );
document.write( "finish it, by telling me in the thank-you note\r\n" );
document.write( "form below.  Then I will get back to you by email.\r\n" );
document.write( "No charge.  I'm a old retired prof.  No charge.\r\n" );
document.write( "I do high school and college math for fun, like \r\n" );
document.write( "other retired people do crossword puzzles for fun.\r\n" );
document.write( "I prefer working math problems and explaining them \r\n" );
document.write( "to kids for fun. \r\n" );
document.write( "\r\n" );
document.write( "Edwin

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