We remark that the converse of the above statement is not true Indeed we have
seen that the function defined by f(x) = |x | is a continuous function Consider the left
hand limit
0–
(0
)
(0)
lim
1
h
f
h
f
h
h
h
→
+
−
=−
= −
The right hand limit
0
(0
)
(0)
lim
1
h
f
h
f
h
h
h
+
→
+
−
=
=
Since the above left and right hand limits at 0 are not equal, 
0
(0
)
(0)
lim
h
f
h
f
h
→
+
−
does not exist and hence f is not differentiable at 0 Thus f is not a differentiable
function