Lecture 22: Local Error of Nystrom & Milne-Simpson Methods
Since for some . But
vanishes also for and . Thus, in view of the fact that has five distinct zeros in the closed interval , the fifth derivative has at least one zero in , the fifth derivative has at least one zero in . We easily find
and thus have, for some
But, by the continuity of it follows as before that
for some between and . Inserting this value in (7.31), (7.29) follows:
for some 
. But 
and 
. Thus, in view of the fact that 
has five distinct zeros in the closed interval 
, the fifth derivative 
has at least one zero in 
it follows as before that 
between 
and 
. Inserting this value in (7.31), (7.29) follows:
