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Math Help - Sketch x^(1/3) * e^-x/3

  1. #1
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    Sketch x^(1/3) * e^-x/3

    I am having trouble finding a compact formula for y'', so that I can place it on my sign table, but instead i got a really long equation which is too big
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  2. #2
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    Quote Originally Posted by SyNtHeSiS View Post
    I am having trouble finding a compact formula for y'', so that I can place it on my sign table, but instead i got a really long equation which is too big
    hi

    Yeah , i tried the second derivative too and ended up with sth really long and uninteresting .

    Fisrtly , find its first derivative which is

    y'(x)=\frac{e^{-\frac{1}{3}x}(x-1)}{3x^{\frac{2}{3}}}

    when y'(x)=0 , x=1

    Make a table calculating dy/dx for 1 , 1^- , 1^+

    this point (1 , \frac{1}{e^{\frac{1}{3}}}) is a local maximum .

    And also the graph passes thought point (0,0)

    Lets take a look at the behaviour of the graph as it goes to +/- infinity

    when x approaches +ve infinity , y approaches 0

    When x approaches -ve infinity , y approaches -ve infinity .

    And it seems that (0,0) is a point of inflexion here .
    Attached Thumbnails Attached Thumbnails Sketch x^(1/3) * e^-x/3-graphs-exponents.jpg  
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  3. #3
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    For my first derivative I got y' = -1/3x ^ (1/3) * e^(-x/3) * (1 - 1 / x). I still dont know a simpler way to find y'' cause the normal way too long.
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