Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward.
I found that y'=-2/x^3, y''=6/x^4. I should set y''=6/x^4=0 and solve for x but what should the answer be?
A) (negative infinity, infinity)
B) (negative infinity, -1)U(1, infinity)
C) (negative infinity, 0)U(0, infinity)
D) (1, infinity)
E) None of these

Question

Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward. 
I found that y'=-2/x^3, y''=6/x^4. I should set y''=6/x^4=0 and solve for x but what should the answer be?
A) (negative infinity, infinity)
B) (negative infinity, -1)U(1, infinity)
C) (negative infinity, 0)U(0, infinity)
D) (1, infinity)
E) None of these

tkhunny · Answer

The second derivative is ALWAYS positive.