Calculus problem- please help me!?

Question

How do you find all the points on the curve y=2x+x^-1 which have a tangent parallel to the x-axis?

Answer 1

set the first derivative=0 and solve for x....the first der gives the slope of the lines tangent to the curve and the x axis has a slope of 0

Answer 2

If the tangent line // the x-axis then the derivative
must be 0 at that point.
So y' = 2 - 1/x² = 0.
x² = 2
x = √2 or x = -√2.
If x = √2, y = 2√2 + 1/√2 = 5/√2.
If x = -√2, y = -5√2.