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Question
Find the intervals in which the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Solution
f(x) = - 2x3 - 9x2 - 12x + 1
f'(x) = -6x2 - 18x - 12 = - 6(x2 + 3x + 2)
= - 6(x + 2)(x + 1)
If f'(x) = 0
-6(x + 2)(x + 1) = 0
x = - 2, -1 divides the real line into three intervals: `(- infty, -2), (-2, -1)` and `(-1, infty)`.
The function f is continuously increasing in the intervals `(- infty, -2)` and `(-1, infty)` and continuously decreasing in (-2, -1).
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