Problems Maxima And Minima Of Function Of Two Variables

Problems Maxima And Minima of Function of Two Variables:

1. Find the extreme value of the functions 2xy - 5x² - 2y² 4x 4y - 6.

Soutions: Let

Solving we get,

The critical point of f is (2/3, 4/3)

Maximum Value;

2. Find the extreme value of the functions x³y² ( 1 - x- y)

Solutions: Let

Hence the critical point are (0,0) and (1/2,1/3)

Hence the Maximum value is given as;