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Idealist

  • 3 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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  1. inkyvoyd
    • 3 years ago
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    x+y=12 seek to optimize (x^3)(y) remember that =12-x

  2. inkyvoyd
    • 3 years ago
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    I mean, y=12-x, sorry.

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

  4. inkyvoyd
    • 3 years ago
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    Remember: you seek to maximize p(x)x^3(12-x) thus you search for where p'(x)=0

  5. inkyvoyd
    • 3 years ago
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    Well, not necessarily always p'(x)=0, but in thsi case you seek it.

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

  7. hcmathkim
    • 3 years ago
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    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

  8. RadEn
    • 3 years ago
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    looks the max value will be 3^7

  9. inkyvoyd
    • 3 years ago
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    @RadEn , both of us were trying to not blurt out the answer :/

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