Answer: We have to find which of the provided functions is not differentiable at x = 0, this means that the slope does not exist at that point, and the derivative when evaluated also does not exist:
The combined plot of the functions:
The plot suggests that the square root must be checked for differentiability at the x = 0, therefore:
[tex]\begin{gathered} f(x)=\sqrt{x} \\ \\ f^{\prime}(x)=\frac{df(x)}{dx}=\frac{1}{2\sqrt{x}} \\ \\ f^{\prime}(0)=\frac{1}{2\sqrt{0}}=\text{ Becomes infinate} \end{gathered}[/tex]
Therefore the derivative does not exist for the square root function at the x = 0, the answer is, Option(B).
