Yesterday I answered a question in a somewhat unsatisfactory way. Today I worked out the kind of answer the questioner really wanted, but now I can't find the question. Question was: g(x) = [f(x)-f(a)]/(x-a) x ≠ a; g(a) = f'(a). Find g'(a). Turns out to be f''(a)/2. The questioner used L'Hospital's rule and asked if it could be done directly. I now have the answer he/she was looking for but cannot find the question.
Maybe you looked at your meta profile. Here are your answer: