Find the Extreme Values of the Function Subject to the Given

question 45

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = x ^ { 2 } + 4 y ^ { 3 } , x ^ { 2 } + 2 y ^ { 2 } = 2$$

• A) Maximum: 8 at (2, 1); minimum: -31 at (1, -2)
• B) Maximum: 8 at (2, 1); minimum: -4 at (0, -1)
• C) Maximum: 4 at (0, 1); minimum: -4 at (0, -1)
• D) Maximum: 4 at (0, 1); minimum: -31 at (1, -2)

---

Definitions:

Gastropods

A large class of mollusks that include snails and slugs, characterized by a single shell (though some are shell-less) and a muscular foot for locomotion.

Ingest Food

The act of consuming food by mouth, initiating the process of digestion.

Sexual Reproduction

A biological process where two cells from different individuals unite to produce the first cell of a new organism.

Embryo Development

The process by which an embryo forms and develops, from fertilization to the fetus stage.