Answer:
Step-by-step explanation:
given is a funciton
f(x,y) = [tex]4xy^2 - x^2y^2 - xy^3.[/tex]
To find extrema of the function in the region enclosed by a triangle with vertices (0,0), (6,0), and (0,6).
At corner points f values are
f(0,0) = 0
f(6,0) = 0
f(0,6) =0
We use partial derivatives to find local extrema
[tex]f_x = 4y^2-2xy^2-y^3\\f_y = 8xy-2x^2y -3xy^2[/tex]
Equate both to 0
We get extrema is at
x=0, y =0
