document.write( "Question 1209075: Find two nonnegative numbers whose sum is 9 and so that the
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Algebra.Com's Answer #847644 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Find two nonnegative numbers whose sum is 9 and so that the
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document.write( "Let the second number be x; then the first number is (9-x),\r\n" );
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document.write( "and we want maximize   = .\r\n" );
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document.write( "Apply Calculus:  take the derivative, equate it to zero, and from this equation find x\r\n" );
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document.write( "    18x - 3x^2 = 0.\r\n" );
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document.write( "We can exclude x= 0, since it is out of our interest, and divide both sides \r\n" );
document.write( "of this equation by  3x.  We will get  simpler equation then\r\n" );
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document.write( "    6 - x = 0\r\n" );
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document.write( "    x = 6.\r\n" );
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document.write( "Take the second derivative  18 - 6x  and evaluate the second derivative at x = 6.  \r\n" );
document.write( "The second derivative value at  x= 6  is  18 - 6*6 = -18.\r\n" );
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document.write( "Since the second derivative is negative at the critical point x= 6, \r\n" );
document.write( "we conclude that x= 6 is the desired point of maximum.\r\n" );
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document.write( "The maximum value of the product is  \r\n" );
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document.write( "     =  = 36*3 = 108.\r\n" );
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document.write( "ANSWER.  The desired numbers are 3 and 6, in this order.\r\n" );
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