if f is a function such that lim h-0 (f(2+h)-f(2))/(h) =5, then which of the following are true?
a. f is continuous at x=2
b. f is differentiable at x=2
c. the derivative of f is continuous at x=2
PLEASE HELP I DON'T UNDERSTAND HOW TO DO THIS!! thanks!!!

Question

if f is a function such that lim h->0 (f(2+h)-f(2))/(h) =5, then which of the following are true?
a. f is continuous at x=2
b. f is differentiable at x=2
c. the derivative of f is continuous at x=2
PLEASE HELP I DON'T UNDERSTAND HOW TO DO THIS!! thanks!!!

anonymous · Answer

$$\lim_{h \rightarrow 0} \frac{ f(2+h)-f(2) }{ h }$$

anonymous · Answer

Hint: That limit is really the derivative of f at x = 2. And that is equal to 5. Also, remember, that if a function is differentiable at a certain point, then it is continuous at that point. (The converse is not necessarily true...i.e. continuity does not imply differentiability).

anonymous · Answer

So you know that Statement I and II must be true from what was said in my last post.

You will need to determine whether the last statement is true or false.