anonymous
  • anonymous
deter if f is differentiable at x=2, i.e., determine if f(2)exist
Mathematics
chestercat
  • chestercat
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JamesJ
  • JamesJ
...if f'(2) exists. What's the function f(x)?
amistre64
  • amistre64
if the limif of f(2) from the right and left match; then we gots diffability
JamesJ
  • JamesJ
No, that's not right.

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amistre64
  • amistre64
really? i must eaither be reading the ? wrong, or remembering this wrong :)
amistre64
  • amistre64
f(x) = |x| is cont, but not diff at x=0 ...
JamesJ
  • 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.
amistre64
  • 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
amistre64
  • amistre64
maybe thats what im remebering :)

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