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.

Question

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..

Steve · Answer

That just means that f"(x) is never zero. There are no points of inflection. visit wolframalpha.com and type in your function. It will show you the graph, and I think your questions will be answered.