if f (x) is not continuous at x = a, then it is if f (x) is continuous at x = a, then it is DIFFERENTIABLE at x = a if f (x) and g (x) are differentiable at x = a, then `f(x)+g(x)` is ALSO differentiable at x = a if a FUNCTION f (x) is continuous at x = a, then `lim_(x to a)f(x)` exists