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ID:
Class: 12
Subject: Math
Topic: Application of Derivative
Type: Short
Question:
Find the intervals in which the function \(f(x) = -2x^3 - 9x^2 - 12x + 1\) is strictly increasing or strictly decreasing.
Official Solution
Explanation:
We have:
\[f'(x) = -6x^2 - 18x - 12 = -6(x + 1)(x + 2)\]
Setting \(f'(x) = 0\):
\[x = -1,\ -2\]
Intervals: \((-\infty, -2),\ (-2, -1),\ (-1, \infty)\)
\[\]
In \((-\infty, -2)\) and \((-1, \infty)\), \(f'(x) < 0\) ⟹ strictly decreasing
\[\]
In \((-2, -1)\), \(f'(x) > 0\) ⟹ strictly increasing
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