Question
The function $(x-\sin x)$ decreases for
✓
Answer
Let $f(x)=x-\sin x$
Differentiating w.r.t. $x$, we get $f^{\prime}(x)=1-\cos x$
For function to be decreasing, $f^{\prime}(x)<0$
$\Rightarrow 1-\cos x<0 \Rightarrow \cos x>1$,
which is not possible, because maximum value of $\cos x$ is 1 .
$\therefore \quad f(x)=(x-\sin x)$ doesn't decrease at any value of $x$.
Differentiating w.r.t. $x$, we get $f^{\prime}(x)=1-\cos x$
For function to be decreasing, $f^{\prime}(x)<0$
$\Rightarrow 1-\cos x<0 \Rightarrow \cos x>1$,
which is not possible, because maximum value of $\cos x$ is 1 .
$\therefore \quad f(x)=(x-\sin x)$ doesn't decrease at any value of $x$.
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