A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0Suppose that f:R to R is differentiable at c and that f(c)=0. Show that g(x):=f(x) is differentiable at c if and only if f'(c)=0.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0\[g'(x)=\frac{f(x)}{f(x)}\cdot f'(x)\]so I guess I'm stuck on showing how to deal with the intederminacy of plugging in x=c=0

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0I guess we must show that\[\frac{f(0)}{f(0)}\neq0\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0can't get l'Hospital to yield anything really...

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[\Large f'(x)=\frac{f(x)f(0)}{xc}f'(c)<\epsilon\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0this is the epsilondelta definition of diff. at c..

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0sorry should be this\[\Large f'(x)=\frac{f(x)f(c)}{xc}f'(c)<\epsilon\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0yeah that looks a bit better...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0oh, @mahmit2012 is here, he can likely help.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354859726253:dw
Ask your own question
Ask a QuestionFind 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.