Two real numbers whose product is a minimum..

[Furizen]

"Find two real numbers whose difference is 40 and whose product is a minimum."

I believe I know how to do this problem when it asks for the MAXIMUM, but asking for the minimum is confusing me..

I've set one number to be x and the other to be (40-x)

f(x)=x(40-x)
f(x)= 40x - x^2 <- Work done so far
f'(x)= 40 - 2x

To be honest I'm not sure if the steps I have done are correct. I've graphed this to find the min/max but I can only find the max.

Please help.

 

[skeeter]

the product is x(x - 40), not x(40 - x) ...

two real numbers whose difference is 40 and whose product is a minimum ...

let x and y be the two real numbers

x - y = 40

y = x - 40

now you'll get a minimum product.

 

[Furizen]

Thank you your replied helped me finally get it