- If
*f*(*x*) = {|*x*| -|*x*-1 |}^{2}, draw the graph of*f(x)*and discuss its continuity and differentiability.**SOLUTION:**We know thatGraphically

*f*(x) could be shown as;From above figure it is clear that

*f(x)*is continuous for*x*∈ ℝ; but*f(x)*is not differentiable at*x*= 0,1⇒

*f*(*x*) is continuous for all x ∈*R*⇒

*f*(*x*) is differentiable for all x ∈*R*- {0, 1} - Discuss the continuity of
*f(x)*= {*x*+ (*x*- [*x*]^{2}} at*x*= 2 and*x*= 2.5, where { } stands for fraction part of*x*and [ ] is greatest integer function. ...

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