# Math Help - derivative question

1. ## derivative question

Hey

my question asks: what is the value of the derivative at f(x) = absolute value x when x =0

Is the answer does not exist because there are no x's left once you do the derivative of /x/ ??? thus the answer is just 1 and cannot be anything else.

thanks

2. Compute $\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)-f(0)}{x-0}$ then, tell us.

3. I would appreciate a straight answer instead of replying me with a question........................... (Quit Doing that it's like my third post in a row where I just get a question as a reply)

F(0) - F(0)/ 0 =

0/0 --> Correct??

I don't get what that has to do with my question.!

4. It has to do with it, if that limit exists, that function should be differentiable at $x=0.$ The limit equals $\underset{x\to 0}{\mathop{\lim }}\,\frac{\left| x \right|}{x},$ then study $\underset{x\to 0^{+}}{\mathop{\lim }}\,\frac{\left| x \right|}{x}$ and $\underset{x\to 0^{-}}{\mathop{\lim }}\,\frac{\left| x \right|}{x}.$

You'll find those limits have different values, thus $\underset{x\to 0}{\mathop{\lim }}\,\frac{\left| x \right|}{x}$ doesn't exist and $f$ is not differentiable at $x=0.$

5. oooo ok thanks very much