Question

So I know a function is not differentiable if the graph has a corner or a cusp, right? I'm still kind of confused on how to tell if a function is differentiable or not; can someone clarify and explain this to me?

Is there any more obvious ways instead of "graphing" the function all the time to see if it has a cusp or corner?

Answer 1

When you take the derivative; effectively what you are doing is finding the tangent of the graph. If the graph has a harp corner, you cannot take the derivative. Notice how in the picture there is more than one possible tangent, or derivative?
I don't know how to tell if there are any sharp corners of a function without graphing it, just put it into wolfram alpha :)

Answer 2

I know that a function is also not differentiable when it has a "vertical tangent", so is this the vertical tangent of the derivative, or the original function?