Question

A quick calc question regarding derivatives.

Answer 1

for a differentiable function f(x) which of the following are true for any x=a

I lim f(x) = lim f (x)
x->a- x->a+

II lim f(x) = f(a)
x->a

III f'(a-) = f'(a+)

IV f(a) = f'(a)

which ones are true?

Answer 2

i now I and III are true, but what about the rest?