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If $f(x)=x(\sqrt{x}-\sqrt{x+1})$ then

$\begin{array}{1 1}(a)\;\text{f(x) is continuous but not differentiable at x=0}\\(b)\;\text{f(x)is differentiable at x=0}\\(c)\;\text{f(x)is not differentiable at x=0}\\(d)\;\text{none of these}\end{array}$

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