Differentiability

Which of the following would be a valid reason the above function is non-differentiable at x = 0?

Graph of a function is given. Where is the function continuous yet NOT differentiable?

The graph of a function is given. Which of the following is not true

Where is the function shown in the graph not differentiable?

Can a function be continuous but not differentiable?

Select all the functions that are continuous and differentiable for all real numbers.

The function shown

On what interval(s) is the following function continuous?

The function, $f\left(x\right)=\frac{x}{x^2-4}$ , is not differentiable at  $x=2$  because the limit of  $f'\left(x\right)$  as x approaches 2 is:  

(a)  

The function, $f\left(x\right)=\frac{x}{x^2-4}$ , is differentiable at  $x=0$  because the limit of  $f'\left(x\right)$  as x approaches 0 is:  

(a)