Extrema of Functions of Two Variables - Multivariable Calc + Calc III Notes
11 27 22
45
relative extremum either relative max or min xo yo
absolute extremum either absolutemax or min xo yo
extreme value theorem If f is definedon a closed
and bounded regionand it's
atyasabsolute extremums closed means that itincludes all of
interior relative extremum rel extreme xo yo t its in interior
boundary relative extremum rel extreme xo yo of dom f
in boundaryof Xo yo
If f has a relative extremum cxo.yo and fx
and fy both exist at xo yo then
If Xo yo 0
This point is considered a critical point Critical points
also occur when one or more of the first partials DNE
Every relative extremum occur at 1 boundary
point of f or 2 critical point of f
Note not every criticalpoint has a relative extremum
points that are critical but no extremum
are called saddle points
Lecture 45 Problems
1 B since c it may not be continuous
2 A 3 D closed and bounded