"Find the range of the function y=x+1/x"?

Question

Can u help me with this maths problem. It's about using differentiation

Answer 1

I don't really see what differentiation has got to do with it.
x + 1/x = y
x^2 - xy + 1 = 0
This has a solution for x if the discriminant is >= 0, ie y^2 - 4 >= 0, ie |y|>=2.
So the range is (-∞,-2] union [2,∞).

Actually, I guess you could differentiate to get y' = 1 - 1/x^2. Making that 0 gives x = 1 or -1, which give y = 2 or -2 respectively.
When 00, so there is a local minimum at (1,2), and for all positive x, y is at least 2.
Similarly when x<-1 you have y'>0, and when -1 Either way you get the same answer.

Answer 2

I'm not sure if you need diffentiation for this problem. After all, the range is just finding the maximun and minimum y values. Use limits instead: The limit as x approaches zero from the right is negative infiniy and the limit as x approaches zero from the right is positvie infinity. Therefore, your range is from - infinity to + infinity