`y = x + 9/x` Identify the open intervals on which the function is increasing or decreasing.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

This function is defined everywhere except x=0 and is differentiable. To determine where it is increasing or decreasing, compute the derivative:

`y'(x)=1 - 9/x^2.`

It is positive in `(-oo, -3) uuu (3, +oo)` and negative in `(-3, 0) uuu (0, 3).` Therefore y is increasing at` (-oo, -3)` and at `(3, +oo)` and y is decreasing at (-3, 0) and at (0, 3).