document.write( "Question 1209926: (a) Let x, y, and z be positive real numbers. Find the largest possible value of
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\n" ); document.write( "\n" ); document.write( "(b) Find \frac{z}{x} if (x,y,z) is a triple that gives the maximum value in Part (a).
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Algebra.Com's Answer #851111 by mccravyedwin(406) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "It doesn't seem obvious to Ikleyn why it works just to substitute x = y = z = 1.\r\n" );
document.write( "Let's forget the means of x,y,z,w.  I was thinking of that to get a starting\r\n" );
document.write( "place to start my thinking from.\r\n" );
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document.write( "(a) Let x, y, and z be positive real numbers.  Find the largest possible value of\r\n" );
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document.write( "To me, it seems obvious that if all three variables approach infinity at the\r\n" );
document.write( "same rate, they will approach \r\n" );
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document.write( "2.489695145 approximately, and that the value could not be higher than that,\r\n" );
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document.write( "Notice that is the same value as substituting 1 for all the variables.  I am not\r\n" );
document.write( "saying that proves anything, just that it starts us to thinking in the right\r\n" );
document.write( "direction.  I still think it's right.  Maybe we could show it rigorously with\r\n" );
document.write( "multivariable calculus by setting the partial derivatives equal zero, and\r\n" );
document.write( "examining the behavior at that point.\r\n" );
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document.write( "(b) Find  if (x,y,z) is a triple that gives the maximum value in Part\r\n" );
document.write( "(a).\r\n" );
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document.write( "Since (1,1,1) is such a triple .   \r\n" );
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document.write( "Edwin

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