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lynda.boyce

  • one year ago

I need some calculus help. the profit (in millions of dollars) derived from selling x units of a certain software is modeled by the following function: P(x) = 0.003x^3 + 100x. If the rate of change in profit, called the marginal profit, is modeled by the derivative of P(x), find P'(x).

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  1. dan815
    • one year ago
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    |dw:1434748999080:dw|

  2. lynda.boyce
    • one year ago
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    can you explain it a little bit?

  3. dan815
    • one year ago
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    |dw:1434749048222:dw|

  4. dan815
    • one year ago
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    do you know first principles?

  5. dan815
    • one year ago
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    where a derivative comes from

  6. lynda.boyce
    • one year ago
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    I have been thrown into this. I haven't taken algebra since high school and calculus is very new to me

  7. dan815
    • one year ago
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    i see

  8. dan815
    • one year ago
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    um start with lines, do you know how to find slope of lines?

  9. lynda.boyce
    • one year ago
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    I sort of understand derivatives

  10. dan815
    • one year ago
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    can you summarize a bit of what u know about derivatives

  11. dan815
    • one year ago
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    id like to know where u stand

  12. lynda.boyce
    • one year ago
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    ok. if you have y = f(x) then the derivative of f is the function whose value is at the x limit

  13. dan815
    • one year ago
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    the way I think is best to think about a derivative is rate of change, it is the slope of the tangent line to some function at every point

  14. lynda.boyce
    • one year ago
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    oh ok I can see that

  15. dan815
    • one year ago
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    if you think about it as this, then the first principle definition of a derivative is very natural

  16. dan815
    • one year ago
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    |dw:1434749793633:dw|

  17. dan815
    • one year ago
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    if you go close and close to the point. the slope of the secant line begins to approach the tangent line at that point

  18. lynda.boyce
    • one year ago
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    yes

  19. dan815
    • one year ago
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    |dw:1434749887083:dw|

  20. dan815
    • one year ago
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    from this, we can write the first principle equation, and see why the power rule comes up

  21. dan815
    • one year ago
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    |dw:1434749924322:dw|

  22. dan815
    • one year ago
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    |dw:1434750070831:dw|

  23. dan815
    • one year ago
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    soo u want to know why the power rule came about?

  24. dan815
    • one year ago
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    when \[f(x) = x^n \] where n is any random number then \[f'(x) = n*x^{n-1}\]

  25. dan815
    • one year ago
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    you can sub in x^n into first principle to see this formula come about

  26. lynda.boyce
    • one year ago
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    I think I have it

  27. dan815
    • one year ago
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    okay :)

  28. lynda.boyce
    • one year ago
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    thank you

  29. dan815
    • one year ago
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    well if you are interested in the proof, you can try to work it out, you will have to use the binomial theorem in there

  30. lynda.boyce
    • one year ago
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    I will try it thanks

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