to check differentiability, the following limit must exist and not only that, check the one-sided limits, they must exist and be equal each other.
I can't figure out how to do this at all. Basically...the GRAPH looks differentiable, and I know from my book that is differentiable, so...shouldn't this one be too? According to my math (taking the limit of both sides)...it's not. I get the left hand limit is -1 and the right hand limit is 0. And I don't get why, or if that's right...?
Problem: Determine whether or not the function is differentiable at x = 0. If so, find .
Also, to do it, I can only use a difference quotient (I haven't learned any fancy shortcuts yet):