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    Question Suppose that g(t)...

    Suppose that g(t)=24te^kt for t> 0,where k is some constant.Find an appropriate value of k .
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    Quote Originally Posted by mathcalculushelp View Post
    Suppose that g(t)=24te^kt for t> 0,where k is some constant.Find an appropriate value of k .

    I think an appropiate value of k could be k = 2, though k = 4 is cutter and k = 345 is, naturally, very handsome.

    Don't you people check your own posts??

    Tonio
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    Quote Originally Posted by mathcalculushelp View Post
    Suppose that g(t)=24te^kt for t> 0,where k is some constant.Find an appropriate value of k .
    k = ln(2)

    The question is extremely vague
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    We need to find the value of k for which g has a horizontal tangent line where t=3.
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    Quote Originally Posted by tonio View Post
    I think an appropiate value of k could be k = 2, though k = 4 is cutter and k = 345 is, naturally, very handsome.

    Don't you people check your own posts??

    Tonio
    Quote Originally Posted by mathcalculushelp View Post
    We need to find the value of k for which g has a horizontal tangent line where t=3.
    That makes more sense

    We need to find g'(3) in other words and for a horizontal line g'(x) = 0

    Use the product rule and the chain rule on g(t)

    Spoiler:
    g(t)=24te^{kt}

    u = 24t \: \rightarrow \: u' = 24

    v = e^{kt} \: \rightarrow \: v' = ke^{kt}

    g'(t) = 24e^{kt} + 24kte^{kt} = 24e^{kt}(1+kt)


    g'(t) = 24e^{kt}(1+kt)

    g'(3) = 24e^{3k}(1+3k) = 0

    In \mathbb{R} 24e^{3k} > 0 so it provides no solutions so 1+3k = 0 which gives k = -\frac{1}{3}
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