Discuss the differentiability of `f(x)=x^3` at `x=1`

Explanation

`f(x)=x^(3)`
`R.f'(1) =underset(hrarr 0)lim (f(1+h)-f(1))/(h)`
`=underset(hrarr0)lim((1+h)^3-1^3)/(h)`
`underset(hrarr0)lim(h^3+3h^2+3h)/(h)`
`underset(hrarr0)lim(h^2+3h+3h)=3`
and L.f(1) `=underset(hrarr0)lim(f(1-h)-f(1))/(-h)`
`underset(hrarr0)lim((1-h)^3-1^3)/(-h)`
`underset(hrarr0)lim(-h^3+3h^2-3h)/(-h)`
`=underset(hrarr0)lim(h^2-3h+3)=3`
`therefore` R.f (1) = L.f (1)
`therefore` f(x) is differentiable at x=1,