Use Lagrange multipliers to find the absolute maximum value and absolute minimum value of f(x, y) = 2x 2 + 2y subject to x 2 + 2y + y 2 = 15.

Maximum absolute value of f=61/2 at () and ()

Minimum absolute value of f=-10 at (0,-5)

Step-by-step explanation:

We are given that

Let

Using Lagrange multipliers

x=0 or

If x=0

Then,

If

If y=-1/2

Then,

Therefore, possible extreme points are

(0,-5),(0,3),() and ()

Therefore, maximum absolute value of f=61/2 at () and ()

Minimum absolute value of f=-10 at (0,-5)