the sum of a number and twice that is number is12. whatis a number?
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Let's call the numbers x and y.
x + 2y = 12, so y = (12-x)/2
xy = (1/2)x(12-x) = -(1/2)x2 + 6x
The graph of f(x) = -(1/2)x2 + 6x is a parabola opening downward.
The function is maximized when x = -6/[2(-1/2)] = 6
Maximum when x = 6 and y = (12-x)/2 = 3
Maximum product = (6)(3) = 18
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go through the attached sheet
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