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

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inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1x+y=12 seek to optimize (x^3)(y) remember that =12x

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1I mean, y=12x, sorry.

Idealist
 2 years ago
Best ResponseYou've already chosen the best response.0x^3(12x), what's the next step? How do I find x and y?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Remember: you seek to maximize p(x)x^3(12x) thus you search for where p'(x)=0

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Well, not necessarily always p'(x)=0, but in thsi case you seek it.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1correction: p(x)=x^3(12x) my apologies openstudy is lagging today and not responding well to my keyboard.

hcmathkim
 2 years ago
Best ResponseYou've already chosen the best response.0y = 12x. f(x) = (x^3)y = (x^3)(12x). 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
 2 years ago
Best ResponseYou've already chosen the best response.0looks the max value will be 3^7

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1@RadEn , both of us were trying to not blurt out the answer :/
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