document.write( "Question 220160: words problem (algebra) find the two real numbers whose sum is 4 and whose product is a minimum \n" ); document.write( "

Algebra.Com's Answer #165343 by stanbon(75887) $\"\"$ $\"About$

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words problem (algebra) find the two real numbers whose sum is 4 and whose product is a minimum
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\n" ); document.write( "Sum: x + y = 4
\n" ); document.write( "Product = xy
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\n" ); document.write( "y = 4-x
\n" ); document.write( "Substitute that into \"Product\" to get:
\n" ); document.write( "P = x(4-x)
\n" ); document.write( "P = 4x-x^2
\n" ); document.write( "That is a quadratic with a = -1, b = 4
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\n" ); document.write( "Comment: That \"Product\" does not have a minimum; it does have a maximum.
\n" ); document.write( "Max occurs at x = -b/2a = -4/(2*-1) = 2
\n" ); document.write( "Maximum product is P = 2*(4-2)= 2*2 = 4
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\n" ); document.write( "Graph of the Product function.
\n" ); document.write( " $\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C4x-x%5E2%29\"$
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\n" ); document.write( "I guess you could say it has a minimum Product
\n" ); document.write( "at x = 0 or x = 4. The Product would be zero.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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