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:

Annual Deposits

Regular sums of money deposited into an account or investment annually.

Equal Annual Withdrawals

Regular, identical amounts of money withdrawn from an investment or savings account over a designated period.

Annuity Due

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Present Value

The current value of a future sum of money or stream of cash flows, given a specified rate of return.