Question

Is there a way to determined differentiability solely from the graph of a function?

Answer 1

Not really. We can guess, but we cannot determine.

Explanation:

Any attempt to deterimine differentiability solely from a graph would require infinitely accurate reading of the graph.

If the function with the following graph differentiable at all `x`?

Answer, No. It is undefined at 2 and has a corner point at 3.

The function is:

`f(x) = {((x-3)^2+2,"if",x<2),((x-3)^2+2,"if",2 < x <=3 ),(0.00000001x+2,"if",x<2) :}`