Among all pairs of numbers whose difference is 10, find a pair whose product is as small as possible. What is the minimum product? a. the pairs of numbers whose difference is 10 and whose product is as small as possible is___ b. The minimum product is___

Question

ranga · Answer

Let one number be x.  The other number can be (x + 10) to give a difference of 10.
Product P = x(x + 10) = x^2 + 10x
For minimum P, find dP/dx = 0 and solve for x.

texaschic101 · Answer

11 - 1 = 10
11 * 1 = 11

I can't seem to find anything smaller

ranga · Answer

The numbers can be positive or negative.
P = x^2 + 10x
dP/dx = 2x + 10 = 0
x = -5
One number is -5 and the other number is +5
Their product is -25  and that is the minimum.

texaschic101 · Answer

oh.....5 - (-5) = 10
         5 * -5 = -25

I didn't think of that

ranga · Answer

You can try any other combination and the product will always be greater than -25.

If they place a restriction that the numbers cannot be negative then the obvious choice is 0 & 10.

texaschic101 · Answer

I get it now.....thumbs up to you ranga :)

ranga · Answer

thank you.