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Math Help - Analysis of graph

  1. #1
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    Analysis of graph

    y = x + square root (absolute value (x))

    what are the first and second derivatives?

    and the extrema, concavity, any asymptotes, continuity?

    I dont even know where to begin
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  2. #2
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    Quote Originally Posted by djdf92 View Post
    y = x + square root (absolute value (x))

    what are the first and second derivatives?

    and the extrema, concavity, any asymptotes, continuity?

    I dont even know where to begin
    The absolute value causes us some problems. To overcome this you should probably analyse the problem for the three seperate cases of x>0, x<0 and x=0.

    Case 1; For x>0
    y=x+\sqrt x
    \therefore y'=1+ \frac {1}{2\sqrt x}
    \therefore y''=\frac {-1}{4\sqrt{x^3}}

    Case 2; For x<0
    y=x+\sqrt {-x}
    \therefore y'=1- \frac {1}{2\sqrt {-x}}
    \therefore y''=\frac {-1}{4\sqrt{{-x}^3}}


    Using these equations you should be able to answer some of the questions above.
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