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Find the interval in which the following function is strictly increasing or strictly decreasing f(x) = 20 – 9x + 6x2 – x3. |
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Answer» f'(x) = 0 ⇒ – 9 + 12x – 3x2 = 0 ⇒ – 3(x2 – 4x + 9) = 0 ⇒ –(3) (x – 1) (x – 3) = 0 ⇒ x = 1, x = 3 ∴ The intervals are (–∞, 1), (1, 3), (3, ∞) So, f(x) is strictly decreasing in (–∞, 1) ∪ (3, ∞) and strictly increasing in (1, 3). |
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