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An example of a function which is continuous everywhere but fails to be differentiable exactly at two point is ____________.

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Toolbox:
  • Every differentiable function is continuous,but the converse is not true.
  • A function is said to be differentiable at every point in its domain.
Consider $f(x)=\mid x\mid$
This function is continuous everywhere but it is not differentiable at $x=1$.
Hence the combined function $f(x)=\mid x\mid+\mid x-1\mid$ is continuous everywhere but not differentiable at exactly $0$ and $1$.
Hence an example of a function which is continuous everywhere but fails to be differentiable exactly at two points is $\mid x\mid,\mid x-1\mid$
answered Jul 4, 2013 by sreemathi.v
 
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