Check monotonicity of f(x) at indicated point:
1) $f (x) = x^{1 / 3}$ at $x = 0$

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Solution

$f (x) = x^{\frac{1}{3}}$
$f^{'} (x) = \frac{1}{3} x^{\frac{- 2}{3}}$
$f^{'} (0) > 0$
Increasing

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