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Question
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
Options
(– 1, ∞)
(– 2, – 1)
(– ∞, – 2)
[– 1, 1]
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Solution
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is (– 2, – 1).
Explanation:
Given,
f(x) = 2x3 + 9x2 + 12x – 1
f'(x) = 6x2 + 18x + 12 = 6(x2 + 3x + 2)
For increasing or decreasing, f'(x) = a
x2 + 3x + 2 = 0
`\implies` x = – 1, – 2
Sign scheme indicates
So the function is decreasing in (– 2, – 1).
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