Find the extreme values of f on the region described bythe inequality.
f(x, y) =2x2 + 3y2 - 4x -2, x2 + y2 ≤ 16
)
(minimum)

The extreme values of a function are the minimum and the maximum values of the function.

The minimum and the maximum values of f are: -4 and 46, respectively.

The given parameters are:

Find the gradient of F(x,y).

Set to 0, to solve for x and y

So, the critical points are:

Calculate the gradients of

Equate the gradients as follows

So, we have:

Divide both sides by 6

Substitute in

Take square roots

So, we have:

Substitute these values in

Hence, the minimum and the maximum values of f are: -4 and 46, respectively.

Read more about extreme values at:

link

step-by-step explanation:

use context clues to figure out the meaning of the bolded word:  

the sage gardener knew when she had to water her plants.  

question 8 options:

mint plant

wise

happy

lazy