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Show that f(x)=x^(1/3) is not differen...

Show that `f(x)=x^(1/3)` is not differentiable at `x=0.`

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For differentiablility at `x=0`
`f’(0)=lim _{x -> 0} frac{f(x)-f(0)}{x-0}`
`=lim _{x -> 0} {x^(1/3)-0}/{x-0}`
`=lim _{x -> 0} {x^(1/3)}/x`
`=lim _{x -> 0} 1/{x^(2/3)}`
This limit does not exist.
`implies f’(0) ` does not exist.
`implies f(x)` is not differentiable at `x=0`.
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