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Show that `f(x) = x^(2/5) ` is not differentiable at x = 0.
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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.
Posted by ishpiro on May 31, 2013 at 2:12 AM (Answer #1)
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