The function `f(x)=-x//2+sinx` defined on `[-pi//3,\ pi//3]` is (a) increasing (b) decreasing (c) constant (d) none of these

Explanation

`f(x)=frac{-x}{2}+sin x` defined on `[frac{-pi}{3}, frac{pi}{3}] `
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therefore f^{prime}(x)=frac{-1}{2}+cos x `
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Rightarrow f^{prime}(x) ge 0 forall x in[frac{-pi}{3}, frac{pi}{3}] `
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{[because text { for } x in[frac{-pi}{3}, frac{pi}{3}], cos x ge frac{1}{2}]}`


Therefore , the given function is increasing .