f'(x) = 3x², so f'(0) = 0. However, f''(x) = 6x, so f''(0) = 0, and the second derivative test is inconclusive. Using the first derivative test, f'(x) = 3x² is positive for x 0. Since the sign of the derivative does not change, there is no extremum. Because f''(x) changes sign at x=0 (from negative for x0), it is a point of inflection.