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Question
On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?
Options
(0,1)
`(pi/2, pi)`
`(0, pi/2)`
None of these
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Solution
None of these
Explanation:
Given f(x) = x100 + sin x - 1,
f'(x) = 100 x99 + cos x
(a) Interval 0 < x < 1, 0 < 100 x99 < 100
And cos x = + positive
`therefore` f'(x) = + positive
Hence, the function f is increasing.
(b) Interval is `pi/2 < "x" < pi`
`therefore` f'(x) = 100 x99 + cos x = + positive
Hence, the function f is increasing.
(c) Interval is, `0 < "x" < pi/2`
Here, 100 x99 and cos x are both positive.
`therefore` f'(x) = + ve
Hence, the function f is increasing.
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