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)

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.