The function (x- x) decreases for - Vidyadip

MCQ

The function $(x-\sin x)$ decreases for

A
all $x$
B
$x<\frac{\pi}{2}$
C
0 < X < $\frac{\pi}{4}$
D
no value of $x$

✓

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 $x$.

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