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Determine whether f(x)=-x/2+sinx is incr...

Determine whether `f(x)=-x/2+sinx` is increasing or decreasing on `(-pi/3,\ pi/3)` .

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We have given
`f(x)=-x/2+sinx`
`f'(x)=-1/2+cosx`
`-pi/3`<`x`<`pi/3`
`(sqrt3)/2`<`cosx`<`(sqrt3)/2`
`(sqrt3)/2`<`cosx`<`1`
`(sqrt3-1)/2`<`cosx-1/2`<`1/2`
`f′(x)`>`0` and `x in (-pi/3.pi/3)`
...
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