Find the absolute maximum and minimum of values of the set d. f(x, y)= 2x^2+y^2-4x-2y+1 d={(x, y) | 0 < = 3, 0 < = y < = 2}

Find the critical points within the region:




So (1, 1) is the only critical point of the function and it happens to fall within the rectangle . At this point, we get a value of .

Now check along the boundaries for potential extreme values.

If , then , which has a maximum when and has a minimum when . So we have a potential extrema at and .

If , then , with a max when and min when . So we have and .

If , then , with a max when and a min when . So we have and .

If , then again, with a max when and a min when . So we have, again, and .

So there are absolute maxima of 7 at (3, 0) and (3,2), and an absolute minimum of -2 at (1, 1).

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.

Idon’t know what the answer is i wish i could