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

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5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10