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Math Help - When is the concentration greatest?

  1. #1
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    When is the concentration greatest?

    The concentration C of insulin in the bloodstream t hours after injection into muscle tissue is

    C(t)=4t/2+t^3

    When is the concentration greatest? t=?
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  2. #2
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    take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.
    Could you help me get the derivative
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  4. #4
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    this derivative is fairly basic ... use the quotient rule and show what you get for a derivative.
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    Quote Originally Posted by skeeter View Post
    this derivative is fairly basic ... use the quotient rule and show what you get for a derivative.
    Is this right? (2+t^3)[4t]-(4t)[2+t^3]
    (2+t^3)(4)-(4t)(3t^2)
    (8t^3)-(12t^3)
    -4t^3
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  6. #6
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  7. #7
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    What do I do with 8-8t^(3)/ (2+t^3)^2
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  8. #8
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    Quote Originally Posted by bgwarhawk View Post
    What do I do with 8-8t^(3)/ (2+t^3)^2
    *Cough*

    Quote Originally Posted by skeeter View Post
    take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.
    So solve 8 - 8t^3 = 0 etc.
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  9. #9
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    Quote Originally Posted by mr fantastic View Post
    *Cough*


    So solve 8 - 8t^3 = 0 etc.
    How do I get t= if I get t^3=1???
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    Quote Originally Posted by bgwarhawk View Post
    How do I get t= if I get t^3=1???
    cube root...
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  11. #11
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    What do I do with the 1?
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  12. #12
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    Quote Originally Posted by bgwarhawk View Post
    What do I do with the 1?
    Quote Originally Posted by skeeter View Post
    take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.
    t = 1 is the critical value in this case and you are checking if there is a maximum. But the idea is the same.
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