Find the local extrema, the open intervals on which the function is increasing, and the open intervals on which the function is decreasing.
f(x)=(x^(1/+2)

now, you get extremas when the derivative is 0, OR
when the derivative is "undefined", when is undefined, you get a "cusp", or an asymptote, so the graph goes to infinity
the derivative is undefined, when the denominator is 0

so, get the critical points from   

so hmm get the critical points from those two cases, and then do a first derivative check in the regions left and right of the critical points

setting the derivative to 0, is easy to see the critical point, is just -1/2

so. you do a first derivative test left and right of that.. like hmmm -0.51 or so... or -3/4  to the left, or  -1/4 to its right

a positive value for the derivative, means is increasing and a negative is decreasing, and the critical point, is well, the extrema :)