$f (x) =1+[cos x]x$, in $0<x≤\frac{π}{2}$

is continuous in $[0,\frac{π}{2}]$ has a maximum value 2 has a minimum value 0 is not differentiable at 2  = x

is continuous in $[0,\frac{π}{2}]$

Since f(x) = 1 in $0<x≤\frac{π}{2}$ [∵ [cos x] = 0] f(x) is continuous in $[0,\frac{π}{2}]$