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cinar
 3 years ago
I have question..
cinar
 3 years ago
I have question..

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cinar
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0I guess we must show that\[\frac{f(0)}{f(0)}\neq0\]

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

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

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

cinar
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0yeah that looks a bit better...

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

mahmit2012
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354859726253:dw
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