lim [(
)]
x
c
x
c
f x
f c
x
c
x
c
→
→
−


−


−


= f′(c) 0 = 0
or
lim
( )
x
c f x
→
 = f (c)
Hence f is continuous at x = c Corollary 1 Every differentiable function is continuous We remark that the converse of the above statement is not true