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)

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation:

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8