Mathematics

Problem

Examine the continuity and differentiability at points

x = 1

and

x = 2

The function

f

defined by

Condition	Definition
$0 \le x < 2$	$x[x]$
$2 \le x \le 3$	$(x-1)[x]$

(where

[ \cdot ]

denotes the greatest integral function less than or equal to

x