I am quite familiar with how to prove differentiability and continuity of functions(by equations).This doubt is to get some meaningful information which I might have missed and it is related to visual inspection of graph plots.
Continuous v/s discontinuous function Graph
With out solving equations, sometimes I can easily identify the non continuity of the graph because there will be breaks in the graph path. There should be non breaking path between any two points in a continuous function
Doubt
An example of graph which is continuous but not differentiable is given below
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Can we identify the non differentiable functions from graph plot as we did earlier in continuity? What I have found is given below
Is this visual inspection method cover all non differentiable cases? If it misses some cases what are those cases?
NB :: I am not looking for a visual inspection method to substitute entirely equation solving method. But I believe if I get such information , some times it may save time