MathematicsIf f(x)=cos⁡π2[x]−x3,−1

If $f (x) = \cos \{\frac{π}{2} [x] - x^{3}\}, - 1 < x < 2 and [x]$ is the greatest integer less than or equal to x, then $f^{'} (\sqrt[3]{\frac{π}{2}})$ is

As we know $1 < \sqrt[3]{\frac{π}{2}} < 2 . If x = \sqrt[3]{\frac{π}{2}} \Rightarrow [x] = 1$

So $f (x) = \cos (\frac{π}{2} - x^{3}) = \sin x^{3} \Rightarrow f' (x) = ({cosx}^{3}) 3 x^{2} \Leftrightarrow f^{'} (\sqrt[3]{\frac{π}{2}}) = 0$

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