In which of the following function Rolle's theorem is applicable ?

Options

A. A) `f(x)={{:(x",", 0le x lt1),(0",",x=1):}" on [0, 1]"`
B. B) `f(x)={{:((sinx)/(x)",", -pilexlt0),(0",",x=0):}" on "[-pi,0]`
C. C) `f(x)=(x^(2)-x-6)/(x-1)" on " [-2, 3]`
D. D) `f(x)={{:((x^(3)-2x^(2)-5x+6)/(x-1)","," if "x ne1),(-6","," if "x=1):}" on "[-2, 3]`

Answer

D