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

Options

A. `f(x)=|x|` in `-2lexle2`
B. `f(x)=tanx` in `0lexlepi`
C. `f(x)=1+(x-2)^(2//3)` in `1lexle3`
D. `f(x)=x(-2)^(2)` in `0lexle2`

Answer

D

Explanation

d. `(a)f(x)=|x|` is not differential at `x=0`
b. `f(x)=tanx` is discontinous at `x=(pi)/2`
c. `f(x)=1+(x-2)^(2//3)` gives real and imaginary value at `x=1`.
d. Only function which satisfies Rolle's theorem is `f(x)=x(x-2)^(2)`in `0lexle2`.