If f(x)=[x]g(x){x}g(x) is a periodic function with period 41 , where g(x) is a differentiable function, then (where {⋅} denotes fractional part of x ).
a. g′(x) has exactly three roots in (41,45)
b. g(x)=0 at x=4k , where k∈I
c. g(x) must be non-zero function
d. g(x) must be periodic function