If the sum of two numbers x and y is 12, what is the maximum product of (x^3)(y)?

Question

inkyvoyd · Answer

x+y=12
seek to optimize (x^3)(y)
remember that =12-x

inkyvoyd · Answer

I mean, y=12-x, sorry.

anonymous · Answer

x^3(12-x), what's the next step? How do I find x and y?

inkyvoyd · Answer

Remember: you seek to maximize p(x)x^3(12-x)
thus you search for where p'(x)=0

inkyvoyd · Answer

Well, not necessarily always p'(x)=0, but in thsi case you seek it.

inkyvoyd · Answer

correction: p(x)=x^3(12-x)
my apologies openstudy is lagging today and not responding well to my keyboard.

anonymous · Answer

y = 12-x.   f(x) = (x^3)y = (x^3)(12-x).  Find the first derivative of f(x). try to find out where x has the absolute maximum. then once u find that x, plug it into y=-x+12 to find y

raden · Answer

looks the max value will be 3^7

inkyvoyd · Answer

@RadEn , both of us were trying to not blurt out the answer :/