SOLUTION: This is about derivatives and continuity. Please help. Let f(x) = x^(1/3) . Then prove that f is not differentiable at O even though it is continuous there. (Show first that it i

Question 1111888: This is about derivatives and continuity. Please help.
Let f(x) = x^(1/3) . Then prove that f is not differentiable at O even though it is continuous there. (Show first that it is continuous).
Thankyou in advance!
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Lim_x->0 ( x^(1/3) ) = 0
f(0) = 0^(1/3) = 0
�
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) = �> f'(0) is undefined (division by zero is undefined).

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