SOLUTION: What is the smallest possible value for the product of 2 real numbers that differ by 6?

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Question 1064107: What is the smallest possible value for the product of
2 real numbers that differ by 6?

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x be the larger number
the smaller number is therefore x-6.

the difference between the numbers will always be 6.

their product would be x * (x-6) = x^2 - 6x.

let y be their product and you get y = x^2 - 6x.

you can use the max/min value formula to get the value of x where y is either max or min.

since the coefficient of the x^2 term is positive, the max/min value will be min.

set y = 0 and the quadratic equation is in standard form of ax^2 + bx = 0

this means that a = 1 and b = 6.

the min/max formula for x is x = -b/2a.

you will get x = -b/2a which becomes x = 6/2 = 3.

when x = 3, the value of y is 9 - 18 = -9.

the minimum value of the product is therefore -9.

here is a graph of the quadratic equation in standard form.