Is a function differentiable at the end points of its domain

Question

Is the function f(x) = x(sqrt(x) + sqrt(x + 9)) differentiable at the point x = 0, which lies at the end point of its domain?
I found differing answers from different sources. Some say it is not even continuous at x=0 while some go on to say that it is continuously differentiable at x=0. What is the right answer?

Answer 1

Yes, it is differentiable at $0$. Note that $f(0)=0$ and that\begin{align}f'(0)&=\lim_{x\to0}\frac{f(x)-f(0)}x\\&=\lim_{x\to0}\sqrt x+\sqrt{x+9}\\&=\sqrt0+\sqrt9\\&=3.\end{align}