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If f(x) = x³ - 3x² + 2, find x where local maximum occurs:

Ax = 2
Bx = 1
Cx = 0
Dx = 3
Answer & Solution
Correct answer: C. x = 0
We have f'(x) = 3x² - 6x. So f'(x) = 3x(x - 2). Critical points x = 0, 2. f''(x) = 6x - 6. f''(0) = -6 < 0 → local maximum at x = 0. f''(2) = 6 > 0 → local minimum.
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