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Discuss the differentiability of f(x)=mi...

Discuss the differentiability of `f(x)=min.{|x|,|x-2|,2-|x-1|}`.

Text Solution

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`becausef(x)=mim.{|x|,y|x-2|,2-|x-1|}`
Draw the graphs of `y=|x|,y=|x-2|andy=2-|x-1|`.

Graph of `y=mim.{|x|,|x-2|,2-|x-1|}` is as follows.

It is clear from the graph that
`f(x)=mim.{|x|,|x-2|,2-|x-1|}` is continuous AAx inR and non-differentiable at `x=-(1)/(2),0,1,2,(5)/(2)`.
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