Given y = 9x + 1/x, find the values of x such that dy/dx=0

We are given y as a function of x, let's first compute dy/dx, and then solve the equation dy/dx =0. dy/dx = 9 -1/x². Then dy/dx = 0 is equivalent to 9 = 1/x². Taking x² on the LHS and 9 on the RHS we obtain x² = 1/9. Finally, the two values of x are -1/3 or 1/3.