Question 1111888
Lim_x->0 ( x^(1/3)  )  = 0  
f(0) =  0^(1/3)  = 0     
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Because f(a) = Lim_x—>a ( f(x) ), and 0 is in the range of f(x),  the function f(x) is continuous at x=0.
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f'(x) = (1/3)x^(-2/3)  =  (1/3) *  ( 1 / (x^(2/3)) )

At x=0, f'(x) = f'(0) = {{{ (1/3)*(1/0) }}}   —>  f'(0) is undefined (division by zero is undefined).