Let f be the function f(x, y) = 4xy2 - x2y2 - xy3. Let D be the triangle with vertices (0,0), (6,0), and (0,6). Find the absolute extrema of function f over region D.

Step-by-step explanation:

given is a funciton

f(x,y) =

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

Equate both to 0

We get extrema is at

x=0, y =0

can i see the following ?

step-by-step explanation: