Question

Show that the function given by f (x) = sin x is
(a) strictly increasing in (0, π/2)
(b) strictly decreasing in (π/2,π)
(c) neither increasing nor decreasing in (0, π)

Answer 1

correct option b

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Answer 2

Step-by-step explanation:

The given function is  f(x)=sinx.

∴f′(x)=cosx

(a) Since for each x∈(0, π/2,),cosx>0⇒f'(x)>0

Hence, f is strictly increasing in (0, π/2 ).

(b) Since for each x∈( π/2,π),cosx<0⇒f′(x)<0.

Hence, f is strictly decreasing in ( π/2,π).

(c) From the results obtained in (a) and (b), it is clear that f is neither increasing nor decreasing in (0,π). so the answer is choice (c).

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