For which interval, the function `(x^2-3x)/(x-1)` satisfies all the conditions of Rolle's theorem

Options

A. `[0,3]`
B. `[-3,0]`
C. `[1.5,3]`
D. for no interval

Answer

D

Explanation

Let `f(x)=(x^(2)-3x)/(x-1)`
`impliesf'(x)=(x^(2)-2x+3)/((x-1)^(2))`
Obviously, it is not derivable at `x=1`, i.e. in (0,3)
Also `f(a)=f(b)` does not hold for `[-3,0]`and `[1,5,3]`