I'm curious about the conditions for when a function f(x) is not differentiable
At a point, or cusp.
At a non-removable discontinuity (such as a jump discontinuity).
On an asymptote.
Probably some other places too.
Also at a place where the slope is vertical.
How about any time it fails the definition of the derivative (i.e., the limit in the definition doesn't exist).
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