If the second derivative is positive at a point, then the graph is concave up at that point, which means that if the first derivative is zero at the same point, then that point must be a local minimum.
As for you are correct that there are two vertical asymptotes, and . Also, is an asymptote for this graph.
To find critical points, you have to calculate the derivative, which is given by the quotient rule:
So x = 0 is a solution; if x is not 0, then we have
Hence there are three possible critical points.