Find the Linearization of the Function at the Given Point $$f ( x , y ) = 8 x ^ { 2 } + 2 y ^ { 2 } + 8 \text { at } ( - 8 , - 3 )$$

question 162

Multiple Choice

Find the linearization of the function at the given point.
- $$f ( x , y ) = 8 x ^ { 2 } + 2 y ^ { 2 } + 8 \text { at } ( - 8 , - 3 )$$

• A) L(x, y) = 16x + 4y + 538
• B) L(x, y) = 16x + 4y - 522
• C) L(x, y) = -128x - 12y - 522
• D) L(x, y) = -128x - 12y + 538

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Definitions:

Consumer Surplus

The discrepancy between the sum consumers are ready and capable of paying for a service or product and the sum they actually spend.

Producer Surplus

The discrepancy between what producers anticipate accepting for a good or service and what they end up being paid.

Imported Units

Refer to products or goods brought into a country from another for sale or use.

Total Surplus

The combined total of consumer and producer surplus, signifying the overall net advantage to society derived from a market transaction.