Refer to the following plot of some level curves of f(x, y) = c for c = −2, 0, 2, 4, and 6. (Each grid square is 1 unit ✕ 1 unit.) The x y-coordinate plane is given. There are five level curves. The level curve labeled −2 consists of two loops, the first in the second quadrant and the second in the fourth quadrant, and this level curve passes through the points (−2, 1.5), (−2, 3), (−3, 2), (2, −1.5), (2, −3), and (3, −2). The level curve labeled 0 consists of two loops, the first in the second quadrant and the second in the fourth quadrant, and this level curve passes through the points (−1, 1), (−1, 3.5), (−2, 0.5), (−2, 3.5), (−3, 0.5), (−3, 3), (1, −1), (1, −3.5), (2, −0.5), (2, −3.5), (3, −0.5), and (3, −3). The level curve labeled 2 consists of the x‐ and y‐axes. The level curve labeled 4 consists of two loops, the first in the first quadrant and the second in the third quadrant, and this level curve passes through the points (1, 1), (1, 3.5), (2, 0.5), (2, 3.5), (3, 0.5), (3, 3), (−1, −1), (−1, −3.5), (−2, −0.5), (−2, −3.5), (−3, −0.5), and (−3, −3). The level curve labeled 6 consists of two loops, the first in the first quadrant and the second in the third quadrant, and this level curve passes through the points (2, 1.5), (2, 3), (3, 2), (−2, −1.5), (−2, −3), and (−3, −2). At approximately which point or points does f appear to attain a maximum value?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Refer to the following plot of some level curves of

f(x, y) = c for c = −2, 0, 2, 4, and 6.

(Each grid square is 1 unit ✕ 1 unit.)

The x y-coordinate plane is given. There are five level curves.

The level curve labeled −2 consists of two loops, the first in the second quadrant and the second in the fourth quadrant, and this level curve passes through the points (−2, 1.5), (−2, 3), (−3, 2), (2, −1.5), (2, −3), and (3, −2).
The level curve labeled 0 consists of two loops, the first in the second quadrant and the second in the fourth quadrant, and this level curve passes through the points (−1, 1), (−1, 3.5), (−2, 0.5), (−2, 3.5), (−3, 0.5), (−3, 3), (1, −1), (1, −3.5), (2, −0.5), (2, −3.5), (3, −0.5), and (3, −3).
The level curve labeled 2 consists of the x‐ and y‐axes.
The level curve labeled 4 consists of two loops, the first in the first quadrant and the second in the third quadrant, and this level curve passes through the points (1, 1), (1, 3.5), (2, 0.5), (2, 3.5), (3, 0.5), (3, 3), (−1, −1), (−1, −3.5), (−2, −0.5), (−2, −3.5), (−3, −0.5), and (−3, −3).
The level curve labeled 6 consists of two loops, the first in the first quadrant and the second in the third quadrant, and this level curve passes through the points (2, 1.5), (2, 3), (3, 2), (−2, −1.5), (−2, −3), and (−3, −2).

At approximately which point or points does f appear to attain a maximum value?

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