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

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

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

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

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

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

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

hcmathkim Group TitleBest ResponseYou've already chosen the best response.0
y = 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
 2 years ago

RadEn Group TitleBest ResponseYou've already chosen the best response.0
looks the max value will be 3^7
 2 years ago

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