Finding critical points

Question

Find all critical points for the function f(x)=x^2 + 54/x

Answer 1

I believe that there is also a critical point at (0,0). Derivative is undefined.

Answer 2

f(x) = x² + 54x^-1

f'(x) = 2x - 54x^-2 = 2x - 54 / x² = (2x³ - 54) / x²

f'(x) = 0 when 2x³ = 54. So, x³ = 27. Therefore, x = 3.

Critical point: (3, f(3)) = (3, 27)