Find the coordinates of the stationary points on the curve y= x+4/x determine the nature of the turning points.Find also the set of values of x for which y increases as as x increases.

Answer 1

dy/dx = 1 - 4/x^2 = 0 for turning points
Solve for x, then find the matching y to find the turning points.
Decide if those points are max or mins using the 2nd derivative test.

y will increase if dy/dx is positive
y will decrease if dy/dx is negative