A value of $\displaystyle k$ such that $\displaystyle f(x)= x^ k$ is $\displaystyle (n-1)$ -times differentiable at $\displaystyle 0$ but not $\displaystyle (n)$ -times differentiable at $\displaystyle 0$ is .
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Hint: $\displaystyle x^{4/3}$ is differentiable at 0. $\displaystyle x^{1/3}$ is not differentiable at 0.
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