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Question
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
Options
(– ∞, 6)
(6, ∞)
(– 6, 6)
(0, – 6)
Solution
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be (– ∞, 6).
Explanation:
f(x) = 5 + 36x – 3x2
Differentiate w.r. to ‘x’
f'(x) = 0 + 36 – 6x
For increasing function
f'(x) > 0
`\implies` 36 – 6x > 0
`\implies` 36 > 6x
`\implies` x < 6
i.e., x ∈ (– ∞, 6)
Hence f(x) increases in (– ∞, 6).
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