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Let X be the lower number.
The problem is: minimize X(X+8).
Let Y=X(X+8)=X2+8X.
The vertex of this parabola is the minimum since it points up.
The X-coordinate of the vertex is -8/2 = -4.
So the minimum product is -4*4 = -16.
Note the two numbers here are -4 and 4.
Verify (using calculus)
dY/dX = 2X + 8 = 0 iff X = -8/2 = -4.
, implies Y = -16.
What else can I help you with?
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What is the minimum product of two numbers whose difference is 22 what are the numbers?
Suppose the smaller of the two numbers is x. Then the other number is x+22. Their product is x*(x+22) = x2 + 22x This has a minimum when 2x = -22 or x = -11. When x = 11, the two numbers are -11 and 11 with a product of -121.
What is the minimum product of two numbers whose difference is 16?
Suppose the smaller of the two numbers is x. Then the larger is x + 16 and their product is x*(x+16) = x2 + 16x This has its minimum when 2x = -16 or x = -8 When x = -8, the two numbers are -8 and 8 and their product is -64.
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What is the minimum product of two numbers whose difference is 22 what are the numbers?
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What is the minimum product of two numbers whose difference is 16?
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