11 27 2245relative extremum either relative max or min xo yoabsolute extremum either absolutemax or min xo yoextreme value theorem If f is definedon a closedand bounded regionand it'satyasabsolute extremums closed means that itincludes all ofinterior relative extremum rel extreme xo yo t its in interiorboundary relative extremum rel extreme xo yo of dom fin boundaryof Xo yoIf f has a relative extremum cxo.yo and fxand fy both exist at xo yo thenIf Xo yo 0This point is considered a critical point Critical pointsalso occur when one or more of the first partials DNEEvery relative extremum occur at 1 boundarypoint of f or 2 critical point of fNote not every criticalpoint has a relative extremumpoints that are critical but no extremumare called saddle pointsLecture 45 Problems1 B since c it may not be continuous 2 A 3 D closed and bounded
