\ \
The member of the family of the function is
. \ \
Find for which members is
largest. \ \
The curvature of the plane at
is
. \ \
Consider
. \ \
Apply derivative on each side with respect to
. \ \
\ \
. \ \
Substitute the corresponding values in
. \ \
\ \
\ \
Substitute
. \ \
\ \
. \ \
\ \
Consider
. \ \
Apply derivative on each side with respect to
. \ \
\ \
\ \
\ \
\ \
\ \
\ \
\ \
Find the critical numbers equate
. \ \
\ \
\ \
. \ \
\ \
\ \
Substitute
values in
. \ \
If
, then
is positive. \ \
If
, then
is negative. \ \
If
, then
is positive. \ \
If
, then
is negative. \ \
The value of
is largest for
. \ \
Therefore, the function is
and
. \ \
\ \
The function is
and
.