A function is a rule that assigns one output to each input. If the derivative is a function, what are its inputs? What are its outputs?

Explain how a function could be continuous at a point but not differentiable at that point. (I know that the weierstrass function is an example but I don't know why.)

If a function is differentiable at every point, is the function continuous?

If you have a function f(x), what is the meaning of f ' (x) and how are they related?

(Ifthe derivative is positive, what do we know about the original function?Why?What if the derivative is negative?)

Thank you!