Answer :

(a) The function is f (x) = sin x


Then, f’(x) = cos x


Since for each x ϵ , cos x > 0, we have f’(x) > 0


Therefore, f’ is strictly increasing in.


(b) The function is f (x) = sin x


Then, f’(x) = cos x


Since for each , cos x < 0, we have f’(x) < 0


Therefore, f’ is strictly decreasing in.


(c) The function is f (x) = sin x


Then, f’(x) = cos x


Since for each x ϵ , cos x > 0, we have f’(x) >0


Therefore, f’ is strictly increasing in……………….(1)


Now, The function is f (x) = sin x


Then, f’(x) = cos x


Since, for each x ϵ, cos x < 0, we have f’(x) < 0


Therefore, f’ is strictly decreasing in …………(2)


From (1) and (2),


It is clear that f is neither increasing nor decreasing in (0, π).


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