I need to know how to do this to find out the derivative of a function as close as possible to an undefined point.
Assume that $f$ is not differentiable at $x=a$.
This might be the same as asking how to evaluate
$\Big(\lim_{h\to 0} \frac{f(x+\delta+h)-f(x+\delta)}{h}\Big) = f'(x+\delta)$
Not sure.
Basically, what's the derivative of a function $f$ at the point closest to $x=a$ if $f$ is not defined at $a$? Note I'm not asking for the derivative of $f(a)$, since that is undefined, but instead the point closest to the undefined point, the endpoint I suppose.
What's the endpoint and what's the derivative of it?
I'm guessing I have to break this into a piecewise function but I'd rather not.