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

Options

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

Answer

D