Question

deter if f is differentiable at x=2, i.e., determine if f(2)exist

Answer 1

...if f'(2) exists.

What's the function f(x)?

Answer 2

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

Answer 3

No, that's not right.

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

maybe thats what im remebering :)