6.5. Differentiable Functions
Examples 6.5.6(a):
We know that f is continuous. To check for differentiability, we have to employ the basic definition:
 f'(x) =
= (
 x    c  ) / (x  c)
 If c > 0 then x > 0 eventually. Then there is no need for the absolute value. The limit become +1.
 If c < 0 then x < 0 eventually. The absolute values are resolved by an additional negative sign. The limit becomes 1.
 If c = 0, then the left and the righthanded limits will be different (1 and +1). Therefore, the function is not differentiable at 0.
This is an example of a function that shows that differentiability
is a stronger concept than continuity:
