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Take a number, x. If it adds to some other number to equal 150, then 150-x is that other number.
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document.write( "We have x and 150-x, and their product must be as large as possible.
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document.write( "Graph it, or remember that it will be a parabola opening down.
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document.write( "Thus, when its derivative equals 0 the function has its maximum.
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document.write( "Subtract 150 from both sides.
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document.write( "Divide both sides by -2
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document.write( "The product of the numbers has its maximum value when x=75. And when x=75 then 150-x = 150-75 = 75.
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document.write( "The two numbers are 75.
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document.write( "You could also solve this by looking at a much smaller number, like 6.
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document.write( "What two real numbers whose sum is 6 have the maximum product?
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document.write( "Compare 3 and 3 with 1 and 5 with 4 and 2 with 6 and 0. The largest product is 3*3.
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document.write( "Look at 5. The largest product comes from 2.5 * 2.5
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document.write( "For 8 the largest product comes from 4*4.
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document.write( "By observation you can see that when the sum is a positive number, then the largest product comes from the number divided by 2.
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document.write( "150/2=75.
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