In which of the following functions is Rolles theorem applicable? `(a)f(x)={x ,0lt=x<1 0,x=1on[0,1]` `(b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-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)ifx!=1,-6ifx=1on[-2,3]`

Options

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

Answer

D