Question

Which of the following functions is not differentiable at x=0?

Answer 1

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:

`\begin{gathered} f(x)=√(x) \\ \\ f^(\prime)(x)=(df(x))/(dx)=(1)/(2√(x)) \\ \\ f^(\prime)(0)=(1)/(2√(0))=\text{ Becomes infinate} \end{gathered}`

Therefore the derivative does not exist for the square root function at the x = 0, the answer is, Option(B).