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

Question

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