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
$\displaystyle y=x+\sqrt x$
$\displaystyle \therefore y'=1+ \frac {1}{2\sqrt x}$
$\displaystyle \therefore y''=\frac {-1}{4\sqrt{x^3}}$
Case 2; For x<0
$\displaystyle y=x+\sqrt {-x}$
$\displaystyle \therefore y'=1- \frac {1}{2\sqrt {-x}}$
$\displaystyle \therefore y''=\frac {-1}{4\sqrt{{-x}^3}}$
Using these equations you should be able to answer some of the questions above.