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

Options

A. `f(x)=|x|` in `-2lexle2`
B. `f(x)=tan x` in `0 le x le pi`
C. `f(x)=1+(x-2)^((2)/(3))` in `1 le x le 3`
D. `f(x)=x(x-2)^(2)` in `0 le x le 2`

Answer

D

Explanation

(a) `f(x)=|x|` is not differentiable at x=0
(b) f(x)=tanx is discontinuous `x=(pi)/(2)`
(c) f(x)=1+`(x-2)^((2)/(3))` gives real and imaginary value at x=1
(d) We have, f(x)=x`(x-2)^(2)`
`f(0)=f(x)`
and f(x) is polynomical function
`thereforef(x)` is continuous and derivative. Rolle's Theorem is applicable.