cinar Group Title I have question.. one year ago one year ago

1. cinar Group Title

Suppose 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.

2. TuringTest Group Title

$g'(x)=\frac{f(x)}{|f(x)|}\cdot f'(x)$so I guess I'm stuck on showing how to deal with the intederminacy of plugging in x=c=0

3. TuringTest Group Title

I guess we must show that$\frac{f(0)}{|f(0)|}\neq0$

4. TuringTest Group Title

can't get l'Hospital to yield anything really...

5. cinar Group Title

$\Large f'(x)=|\frac{f(x)-f(0)}{x-c}-f'(c)|<\epsilon$

6. cinar Group Title

this is the epsilon-delta definition of diff. at c..

7. cinar Group Title

sorry should be this$\Large f'(x)=|\frac{f(x)-f(c)}{x-c}-f'(c)|<\epsilon$

8. TuringTest Group Title

yeah that looks a bit better...

9. TuringTest Group Title

oh, @mahmit2012 is here, he can likely help.

10. mahmit2012 Group Title

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