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14.7 Maxima & Minima of Functions of Two Variables ( , )f x y has a local maximum at
 

Summary: 14.7 Maxima & Minima of Functions of Two Variables
1
( , )f x y has a local maximum at
( )0 0,x y if 0 0( , ) ( , )f x y f x y for
all points near ( )0 0,x y
( , )f x y has a local minimum at
( )0 0,x y if 0 0( , ) ( , )f x y f x y for
all points near ( )0 0,x y
( , )f x y has an absolute minimum at
( )0 0,x y if 0 0( , ) ( , )f x y f x y for
all the points in domain of ( , )f x y
( , )f x y has an absolute maximum at
( )0 0,x y if 0 0( , ) ( , )f x y f x y for
all the points in domain of ( , )f x y
If f has either local (absolute) max. or min., we call f has local (absolute)
extremum.
Main question:
How to find relative or absolute extrema?
Finding Relative Extrema of z=f(x,y)
2

  

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

 

Collections: Mathematics