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Math Help - maximum and minimum

  1. #1
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    Exclamation maximum and minimum

    The amount of current in an electrical system is given by the function
    c(t)= -t^3 + t^2 + 21 t, where t is time in seconds and 0<t<5. Determine the times at which the current is maximal and minimal, and the amount of current in the system at these times.
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  2. #2
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    Quote Originally Posted by math123456 View Post
    The amount of current in an electrical system is given by the function
    c(t)= -t^3 + t^2 + 21 t, where t is time in seconds and 0<t<5. Determine the times at which the current is maximal and minimal, and the amount of current in the system at these times.
     -t^3+t^2+21t
     \frac{dy}{dx} = -3t^2+2t+21=0
    3t^2-2t-21=0 = (t+3)(3t+7)
    t=3 or t=\frac{-7}{3}
    If you differentiate 3t^2-2t-21 again to get the maximum and minimum you get 6t-2. So if you put in t=3, then 6t-2 is positive, therefore it is a minimum. If you put in t =-7/3 then 6t-2 is negative, so that is a maximum.

    Oh right, I didn't see that it said 0<t<5. In that case the smallest possible value you can get in that range is t=0.
    Last edited by ThePerfectHacker; March 11th 2009 at 09:58 PM.
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