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

The minimum value of the function is at the point and the maximum value of the function is at the points .

So, critical points of is .

Put this in .

.

So, critical point is in the interior point of the given region.

Let there is a parameter such that and .

and

So, and

So,

So,

Put in , to determine the value of .

So, the obtained possible extrema are .

Now, find at and .

So, the minimum value of the function is at the point and the maximum value of the function is at the points .

Learn more about extrema here:

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c. 1,233 miles

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