Does Continuity Imply Differentiability?

Investigate each of the four continuous functions in the app. Notice that each of them have a point of interest on the x-axis with a secant line drawn from this point to a dynamic arbitrary point on the graph of the function. Move the arbitrary point to see what happens to the secant line and its slope as the arbitrary point approaches the point of interest. Is the function differentiable at the point of interest? If not, why not?