document.write( "Question 214564: Not sure which topic would fit this best... but if someone could show me how to tackle this question:\r
\n" ); document.write( "\n" ); document.write( "The sum of two numbers is 30 and their product is a maximum. Find the two numbers. \n" ); document.write( "
Algebra.Com's Answer #162045 by Alan3354(69443)\"\" \"About 
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Not sure which topic would fit this best... but if someone could show me how to tackle this question:
\n" ); document.write( "The sum of two numbers is 30 and their product is a maximum. Find the two numbers.
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\n" ); document.write( "It's always the square, in this case 15 and 15.
\n" ); document.write( "15*15 = 225
\n" ); document.write( "14*16 = 224
\n" ); document.write( "13*17 = 221
\n" ); document.write( "See the pattern?
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\n" ); document.write( "A rigorous solution:
\n" ); document.write( "x*(30-x) = 0
\n" ); document.write( "x^2 - 30x = 0
\n" ); document.write( "The vertex (maximum) is at x = -b/2a
\n" ); document.write( "= 30/2 = 15
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\n" ); document.write( "Using calculus:
\n" ); document.write( "f(x) = x*(30-x)
\n" ); document.write( "f(x) = x^2 - 30x
\n" ); document.write( "f'(x) = 2x-30 = 0
\n" ); document.write( "2x-30 = 0
\n" ); document.write( "x = 15
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