f(x)=x+1/x

Find all critical numbers. Find where the function is increasing and decreasing. Find critical points and identify each as a relative maximum, relative minimum, or neither.
Find second order critical numbers and tell where the graph is concave up and where it is concave down.

I'm on the last question now, but i don't know how to find the zeros of the second derivative because i got 2/x^3..i need it to find critical numbers and tell where the graph is concave up and where it is concave down.

Since the second derivative is [latex] \frac{2}{x^3} [/latex] , it's negative when [latex] x<0 [/latex] and positive when [latex] x>0 [/latex] , so the graph is concave up at (0, [latex] \infty[/latex]), and it's concave down at ([latex] -\infty[/latex], 0).

ok thanks:)