Homework Help

Show that `f(x) = x^(2/5) `  is not differentiable at x = 0.

user profile pic

jjmgingrich | Student, Undergraduate | Salutatorian

Posted May 31, 2013 at 1:32 AM via web

dislike 1 like

Show that `f(x) = x^(2/5) `  is not differentiable at x = 0.

1 Answer | Add Yours

user profile pic

ishpiro | Teacher | (Level 2) Associate Educator

Posted May 31, 2013 at 2:12 AM (Answer #1)

dislike 0 like

Let's try to take the derivative of `f(x) = x^(2/5)` using power rule:

`(x^n)' = nx^(n-1)`

Here, `n= 2/5` , so

`f'(x) = 2/5 x^(-3/5) = 2/5* 1/x^(3/5)`

This function is not defined at x = 0 (the denominator cannot be 0), so the derivative does not exist at x = 0. Thus, the function is not differentiable.

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes