A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
I don't get the proof of Differentiable implies continuous. We prove that lim f(x) as x tends to x0  f(x0) = 0 (which is the definition of continuous) by manipulating it to be f'(x) * 0. I don't see how this completes a proof. This just proves that f is continuous. In fact, in the accompanying notes it says that this shows "it’s true that lim f(x) (as x tends to x0) −f(x0) = 0, and it’s true that diﬀerentiable functions are continuous." I don't see where differentiable implies continuous in all of this. What am I missing?
anonymous
 3 years ago
I don't get the proof of Differentiable implies continuous. We prove that lim f(x) as x tends to x0  f(x0) = 0 (which is the definition of continuous) by manipulating it to be f'(x) * 0. I don't see how this completes a proof. This just proves that f is continuous. In fact, in the accompanying notes it says that this shows "it’s true that lim f(x) (as x tends to x0) −f(x0) = 0, and it’s true that diﬀerentiable functions are continuous." I don't see where differentiable implies continuous in all of this. What am I missing?

This Question is Closed

beginnersmind
 3 years ago
Best ResponseYou've already chosen the best response.1I'm not sure what the question is. Starting from the assumption that f is differentiable at f(x0) and proving that it's continuous at f(x0) does prove that differentiability implies continuity. That's what implication means.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Haha yeah I thought about it some more and see it now. It was a long day when I asked the question. Continuous means that the (derivative of f(x))  f(x0) = 0 and it's legimate to subtrace that f(x0) from any differentiable function. But doing that we see when end up the fact that it equals zero so we know any differentiable function is continuous at x0
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.