Among all pairs of numbers whos difference is 12, find a pair whose product is as small as possible. what is the minimum product?

Let x be one of the numbers. Because their difference is 12, the second number should be x - 12. Their product is,

x (x - 12) = P

x² - 12x = P

Differentiate both sides and equate to zero.

2x - 12 = dP/dt = 0

The value of x is equal to 6. The second number is - 6.