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Math Help - Marginal Profit

  1. #1
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    Marginal Profit

    A certain item sells for $30. If the cost of producing this item is given by C=.05x^3+100, find the marginal profit when x=10.

    So i know P(rofit)=R-C and marginal Profit =dP/dx
    but im not sure how you find R and when you plug in 10 for x and $30

    Please Help
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  2. #2
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    Revenue will be price times number sold, so...



    ... where straight lines differentiate downwards with respect to x.

    Spoiler:


    Obviously plug in for x now, in the derivative expression.


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  3. #3
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    I don't know how you got the 30x-1/2x^3-100
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  4. #4
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    Quote Originally Posted by rawkstar View Post
    I don't know how you got the 30x-1/2x^3-100
    Some of it's R and some of it's C...
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  5. #5
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    Quote Originally Posted by tom@ballooncalculus View Post
    Some of it's R and some of it's C...

    man Tom...nice style with the spoliers and all that. what prime pedagogy.
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  6. #6
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    howd u get R?
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  7. #7
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    Quote Originally Posted by tom@ballooncalculus View Post
    Revenue will be price times number sold, so...
    .....
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  8. #8
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    thanks but shouldnt P=30x-.05x^3-100 since C=.05x^3+100?
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  9. #9
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    Quote Originally Posted by rawkstar View Post
    thanks but shouldnt P=30x-.05x^3-100 since C=.05x^3+100?
    Gosh, yeah - never saw that zero!

    Will correct the pics
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