Find the Absolute Maxima and Minima of the Function on the Given

question 344

Multiple Choice

Find the absolute maxima and minima of the function on the given domain.
- $$f ( x , y ) = x ^ { 2 } + 12 x + y ^ { 2 } + 16 y + 10 \text { on the rectangular region } - 1 \leq x \leq 1 , - 2 \leq y \leq 2$$

• A) Absolute maximum: 74 at (2, 2); absolute minimum: 10 at (0, 0)
• B) Absolute maximum: 74 at (2, 2); absolute minimum: -29 at (-1, -2)
• C) Absolute maximum: 59 at (1, 2); absolute minimum: -29 at (-1, -2)
• D) Absolute maximum: 59 at (1, 2); absolute minimum: 10 at (0, 0)

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Definitions:

Many Generations

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Darwin's Principles

Fundamental concepts proposed by Charles Darwin, including natural selection and survival of the fittest, explaining the evolution of species.

Evolution

The procedure through which diverse living entities are presumed to have originated and varied from previous types over the course of the earth's existence.

Population Variation

The differences in phenotypes and genotypes within a group of individuals, often studied in genetics and ecology.