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  4. If [x] represents the greatest integer function and f (x) = x - [x] - cos x then f’ ( (π/2) ) =

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Q. If [x] represents the greatest integer function and f (x) = x - [x] - cos x then f’ $\left( \frac{\pi}{2} \right)$ =

KCETKCET 2019Limits and Derivatives

Solution:

$f\left(x\right)=x-\left[x\right]-cos x$
$f '\left(x\right)=1+sin x$
$f '\left(\frac{\pi}{2}\right)=1+1=2$