anonymous
  • anonymous
If the sum of two numbers x and y is 12, what is the maximum product of (x^3)(y)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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inkyvoyd
  • inkyvoyd
x+y=12 seek to optimize (x^3)(y) remember that =12-x
inkyvoyd
  • inkyvoyd
I mean, y=12-x, sorry.
anonymous
  • anonymous
x^3(12-x), what's the next step? How do I find x and y?

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inkyvoyd
  • inkyvoyd
Remember: you seek to maximize p(x)x^3(12-x) thus you search for where p'(x)=0
inkyvoyd
  • inkyvoyd
Well, not necessarily always p'(x)=0, but in thsi case you seek it.
inkyvoyd
  • inkyvoyd
correction: p(x)=x^3(12-x) my apologies openstudy is lagging today and not responding well to my keyboard.
anonymous
  • anonymous
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
  • RadEn
looks the max value will be 3^7
inkyvoyd
  • inkyvoyd
@RadEn , both of us were trying to not blurt out the answer :/

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