Increment Theorem (Sufficient condition for differentiability):
For some both and exist at all points in
Let . Applying Mean Value Theorem to the functions we can find points between and and between and such that ............................. (26)
.............................. (27) Thus, using (26) and (27) we have
where Since are continuous at , we obtain Hence, is differentiable at
and 
be such that the following hold: 
both 
and 
exist at all points in 
and 
are continuous at the point 
. Then, 
is differentiable at 
. 
. Applying Mean Value Theorem to the functions 
between 
and 
and 
between 
and 
such that 
............................. (26) 
.............................. (27) 
are continuous at 
, we obtain 
is differentiable at 
