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  4. The function f(x) = cos x is strictly decreasing on

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Q. The function $ f(x) = \cos x $ is strictly decreasing on

AMUAMU 2017

Solution:

Let $f(x)=\cos x$
$\Rightarrow f^{\prime}(x)=-\sin x$
For strictly decreasing, $f^{\prime}(x)< 0 \Rightarrow-\sin x< 0$
$\Rightarrow \sin x >0$, which is true for all $x \in(0, \pi)$