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If f(x)=x^(1//3)(x-2)^(2//3) for all x ,...

If `f(x)=x^(1//3)(x-2)^(2//3)` for all `x ,` then the domain of `f'` is `x in R-{0}` b. `{x|x>>0}` c. `x in R-{0,2}` d. `x in R`

A

` x in R-{0}`

B

`{x|xgt0}`

C

`x in R-{0,2}`

D

`x in R`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x^(1//3)(x-2)^(2//3)`
`therefore" "f'(x)=x^(1//3).(2)/(3)(x-2)^(-1//3)+(x-2)^(2//3).(1)/(3)x^(-2//3)`
`=(1)/(3)x^(-2//3)(x-2)^(-1//3)(3x-2)`
`therefore` f' is not denined at x= 0 and at x = 2
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