Verify Lagranges mean value theorem for `f(x)=x-2sinx` on `[-pi,\ pi]`

Explanation

`f(x) =x-2 \sin x,(-\pi, \pi) `

`f^{\prime}(c) =\frac{f(\pi)-f(-\pi)}{\pi-(-\pi)}`

=`\frac{(\pi-0)-(-\pi-0)}{2 \pi}=\frac{2 x}{2 \pi}=1` .

`f^{\prime}(x)=1-2 \cos x` .

`1-2 \cos x=y`

`-2 \cos =0`

`\cos x=0` .

`\therefore x=\pi / 2` .