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Critical points are where the derivative is zero or undefined. For a polynomial they are the roots of f', found here by sign-change bisection, and the second derivative test classifies each as a maximum or minimum.
Critical point
f'(x) = 0; f''(x) > 0 gives a minimum, f''(x) < 0 a maximum
f' = 3x² − 6x − 9 = 3(x − 3)(x + 1), so the critical points are x = −1 (maximum) and x = 3 (minimum).
The test is inconclusive; check the sign of f' on either side, or use higher derivatives.