The question is quite pertinent and so is
its answer If  
0
(
)
( )
lim
h
f c
h
f c
h
→
+
−
 does not exist, we say that f is not differentiable at c In other words, we say that a function f is differentiable at a point c in its domain if both
–
0
(
)
( )
lim
h
f c
h
f c
h
→
+
−
 and 
0
(
)
( )
lim
h
f c
h
f c
h
+
→
+
−
 are finite and equal A function is said
to be differentiable in an interval [a, b] if it is differentiable at every point of [a, b]