Show that the function given by $f (x) = s i n x$ is
neither increasing nor decreasing in $(0, π)$

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Solution

When $x ϵ (0, π)$ . We see that $f^{'} (x) > 0$ in (0, $\frac{π}{2}$ ) and $f^{'} (x) < 0 i n (\frac{π}{2}, π)$
So, f'(x) is positive and negative in $(0, π)$ .
Thus, f(x) is neither increasing nor decreasing in $(0, π)$

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