On which of the following intervals is the function f given by `f(x)=x^(100)+sinx-1`strictly decreasing ?
(A) (0, 1)
(B) `(pi/2,pi)`
(C) `(0,pi/2)`
(D) None of these

Explanation

We have,

`f(x)=x^100+sinx-1`

`impliesf'(x)=100x^99+cosx`

In the interval `(0,1)`,`cosx>0` and `100x^99>0`.

`f'(x)>0`

thus , the function f is strictly increasing in interval `(0,1)`

In the inetrval `(pi/2,pi)`,`cosx<0` and `100x^99>cosx`

`f'(x)>0` in `(pi/2,pi)`

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