An absolute maximum is also a local maximum. Being the largest value overall, it is also the largest value in its immediate neighborhood. Hence, a list of all local maxima will automatically include the absolute maximum if there is one. Similarly, a list of all local minima will include the absolute minimum if there is one.
L'Hôpital's Rule
a. First Form
Suppose that , that
and
exist, and that
. Then
b. Stronger Form
Suppose that , that
and
are differentiable on an open interval I containing
, and that
on I if
Then
,
assuming that the limit on the right side exists.
Proof of L'Hôpital's Rule
Find
Solution
