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On which of the following intervals is t...

On which of the following intervals is the function `x^(100)+sinx-1` decreasing? `(,pi/2)` (b) `(0,1)` `(pi/2,pi)` (d) none of these

A

`(0, pi//2)`

B

`(0,1)`

C

`(pi//2,pi)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`f.(x) = 100x^(99) + cos x`
f.(x) `gt` 0 in `x in (0,(pi)/(2))`
`f.(x)gt0" " "in" " "x in(0,1)`
`f.(x)gt0 " ""in" " " x in ((pi)/(2),pi)`
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