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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24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.