6.5. Differentiable Functions

Examples 6.5.6(a):

The function f(x) = | x | is continuous everywhere. Is it also differentiable everywhere ?

We know that f is continuous. To check for differentiability, we have to employ the basic definition:

Your browser can not handle Java applets This is an example of a function that shows that differentiability is a stronger concept than continuity:
  • every differentiable function is continuous (theorem)
  • there are continuous functions that are not differentiable
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