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. Share with your friends Share 22 Devesh Kumar answered this ⇒fx= -2x for x<-1 2 for -1≤x<1 2x for x≥1LHD=lim x→-1-fx-f-1x--1LHD=lim x→-1--2x-2x+1LHD=lim x→-1--2x-2x+1LHD=lim x→-1--2x+1x+1LHD=lim x→-1--2 = -2RHD=lim x→-1+fx-f-1x--1RHD=lim x→-1+2-2x+1 = 0LHD at x = -1 ≠ RHD at x = -1,so function is not differentiable at x = -1Similarly, we can prove that given function is not differentiable at x = 1.. 66 View Full Answer Kartik Goel answered this 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 -16
