Question

If $\left[x\right]$ represents the greatest integer function and $f\left(x\right)=x–\left[x\right]–\cos x$ then $f^{\prime }\left(\frac{\pi }{2}\right)=$

• A. $2$
• B. $0$
• C. $\text{does not exist}$
• D. $1$

Answer 1

The correct option is A $2$

$f\left(x\right)=x–\left[x\right]–\cos xWeknow,1<\frac{\pi }{2}<2,So,f\left(x\right)=x-1-\cos x{f}^{\prime }\left(x\right)=1+\sin x{f}^{\prime }\left(\frac{\pi }{2}\right)=1+\sin \frac{\pi }{2}=2$