f (x) = [sin x] + [cos x], x ∈ [0, 2π], where, [.] denotes the greatest integer function. Total number of point where f (x) is non-differentiable is equal to:

5

$\left\{\begin{matrix}0&0<x<π/2\\-1&π/2<x<π\\-2&π<x<3π\\-1&3π/2<x<2π\\1&x=π/2\\-1&x=π\\-1&x=3π/2\\1&x=0,2π\end{matrix}\right.$

f(x) is discontinuous and hence non-differentiable at 5 points. (x = 0, π/2, π, 3π/2, 2π)