Question

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

• A. 2
• B. 0
• C. does not exist
• D. 1

Answer 1

Answer: (A)

$f\left(x\right)=x-\left[x\right]-cosx$
$f^{\prime }\left(x\right)=1+sinx$
$f^{\prime }\left(\frac{\pi }{2}\right)=1+1=2$