# show that the function f(x)=|x-1|+|x+1|, for all x belongs to R is not differentiable at the point x= -1 and x=1.

• 66
f(x)= -2x for x<-1 , 2 for x belongs to -1 to 1 and 2x for x>1
at x=-1 f(x-h)=-2(x-h)-(-2x)/-h =-2  and f(x+h ) =2-2/h=0at x=-1  thus RHD doesnt equals LHD thus function is not differentiable at x=-1 similarly it is not differentiable at x=1 . also from graph we see that function has sharp edge at these points thus not differentiable
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