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## Homework Statement

The chapter that I am reading is on continuity and talking about how inorder for a graph to have a derivative at some point say (x,y)... the limit as delta(y)/delta(x) must approach zero... If the limit approaches zero that means the graph is continuouse at point (x,y) therefore there is a derivative at that point....... Please correct me if I am wrong....

Anyways my real question is in the attachemnt.... can some one please help me understand... thank you.

Sorry the picture is small... the question is ..... is there another explanation why there is no derivative at point (x,y) ....( in the picture) other than because the graph at that given point changes directions abruptly.....?