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Math Help - First and Second Derivatives and other aspects of a function

  1. #1
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    First and Second Derivatives and other aspects of a function

    f(x)= 5xe^-.2x

    Domain of the function = All real numbers
    Intercepts: x=0 y=0
    Vertical asymptote = none
    Horizontal asymptote = y=0
    Find f'(x) = 5/.2e^.2x

    Let me know if I'm doing anything wrong so far. Thanks, appreciate all help
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  2. #2
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    Everything looks fine except for the derivative.

    f(x) = 5xe^{\frac{-x}{5}}
    \implies f'(x) = 5e^{\frac{-x}{5}} + 5x\frac{-1}{5}e^{\frac{-x}{5}} by the product rule.

    It can be simplified further.
    Last edited by n0083; March 29th 2009 at 09:44 PM. Reason: wrote f(x) = f'(x), I meant implies
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  3. #3
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    Thanks, mind simplifying for me?
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  4. #4
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    I also need 2nd derivative.
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  5. #5
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    Quote Originally Posted by Zabulius View Post
    Thanks, mind simplifying for me?
    Why don't you try it and show me your result?
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  6. #6
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    (5e^-x/5)(1+-1/5x)
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  7. #7
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    Quote Originally Posted by Zabulius View Post
    (5e^-x/5)(1+-1/5x)
    Let's try again

    f'(x) = 5e^{\frac{-x}{5}} + 5x\frac{-1}{5}e^{\frac{-x}{5}} \implies e^{\frac{-x}{5}} (5-x)
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