Yep, that's correct, no stationary points within the reals.
For the second question, what did you get as the derivative?
I have a couple of questions.
First, if the first derivative of a function is a quadratic can I show that the function has no stationary points by showing that the discriminant of the first derivative is less than zero?
Second, how do I go about finding the range of the values of a for which
y = x - (a/x) has no stationary points.
I know the answer is that a is greater than or equal to zero, but I don't know how to get there.