alleryFor f(x) = x³ - 3x² + 4, the function is increasing on intervals:
A(-∞, 0)
B(2, ∞)
C(0, 2) only
D(-∞, 0) ∪ (2, ∞) (where f'(x) = 3x(x-2) > 0)
Answer & Solution
Correct answer: D. (-∞, 0) ∪ (2, ∞) (where f'(x) = 3x(x-2) > 0)
We have f'(x) = 3x² - 6x.
So f'(x) = 3x(x - 2).
f' > 0 when x < 0 OR x > 2 (increasing).
f' < 0 on (0, 2) (decreasing).
Local max at x = 0, local min at x = 2.
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