I am reviewing all of my notes where we have a piecewise function, and I see everytime we check for differentiability, we check for continuity first. For example I will show you problem.

I do not understand why do we check continuity first always, if the theorem holds that if it is differentiable, then it is continuous. , therefore if no continuty = no differentiation??

Is there anyway I can check for differentation first?

m.imgur.com/gtcEr2q