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Question
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
Options
(– 2, 2)
(– ∞, – 2) ∪ (2, ∞)
(– 2, ∞)
(– ∞, 2)
Solution
(– ∞, – 2) ∪ (2, ∞)
Explanation:
Here, f(x) = x3 – 12x
f'(x) = 3x2 – 12
For increasing f'(x) > 0
∴ 3x2 – 12 > 0
3(x2 – 4) > 0
3(x – 2)(x + 2) > 0
∴ x > 2, – 2
∴ For x = – 3
f'(– 3) = 3(– 3)2 – 12
= 15 > 0
For x = 3
f'(3) = 3(3)2 – 12
= 15 > 0
∴ f(x) is increasing in interval (– ∞, – 2) ∪ (2, ∞)
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