$3$

Mark for Review

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Consider the curve in the $xy-$plane defined by $y\sqrt[\phantom{2}]{y^3+1}=x$ for $y>-1.$ For what value of $y,y>-1,$ does the derivative of $y$ with respect to $x$ not exist?

$y=(-\frac{1}{4}{)}^{\frac{1}{3}}$

$y=0$

The derivative of $y$ with respect to $x$ exists for all $y>-1.$