## anonymous 4 years ago deter if f is differentiable at x=2, i.e., determine if f(2)exist

1. JamesJ

...if f'(2) exists. What's the function f(x)?

2. amistre64

if the limif of f(2) from the right and left match; then we gots diffability

3. JamesJ

No, that's not right.

4. amistre64

really? i must eaither be reading the ? wrong, or remembering this wrong :)

5. amistre64

f(x) = |x| is cont, but not diff at x=0 ...

6. JamesJ

A real valued function $$f$$ is differentiable at $$x = a$$ if the limit $\lim_{x \rightarrow a} \frac{f(x)-f(a)}{x-a}$ exists. Or equivalently, if the limit $\lim_{h \rightarrow 0} \frac{f(a+h) - f(a)}{h}$ exists.

7. amistre64

the derivative of f(x)=|x| from the left is -1, and from the right is +1; so at zero the derivative is both -1 and +1 which is inconsistent ... hmmmm

8. amistre64

maybe thats what im remebering :)