Find two real numbers whose sum is 24 and whose product is minimum.

Question

mathstudent55 · Answer

Do you mean a mimimum or a maximum?

anonymous · Answer

minimum :)

mathstudent55 · Answer

I don't think there can be a minimum in this probelm.

anonymous · Answer

Hmm, i see. That's what i've been thinking of. Well, thank yoooou so much for the help @mathstudent55 ^_^v

mathstudent55 · Answer

This problem will give you a function whose graph is a parabola that opens downward, so it has a maximum value, but it extends downard for ever. There is no minimum value.

anonymous · Answer

Hmm. Okaaaay :) thank you for your explaination @mathstudent55 and thank you for your help so much! ^_^ you really helped alot. Arigato gozaimas. ^_^v

mathstudent55 · Answer

Let on number by x
The other number is 24 - x

Their product is x(24 - x) = 24x - x^2
y = -x^2 + 24x
has a vertex at x = 24-2 = 12
The _maximum_ product is when both numbers are 12.