Suppose That $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$

question 65

Multiple Choice

Suppose that $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$ Find a normal vector to the tangent plane of f at the point (1, 1) .Select all that apply.

• A) \(5 \vec { i } + 5 \vec { j } - \vec { k }\)
• B) \(5 \vec { i } + 5 \vec { j } + \vec { k }\)
• C) \(- 5 \vec { i } - 5 \vec { j } + \vec { k }\)
• D) \(- 5 \vec { i } + 5 \vec { j } + \vec { k }\)

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Definitions:

Producer Surplus

The difference between the amount producers are willing to accept for a good or service versus what they actually receive.

Subsidies

Financial support provided by governments to individuals, businesses, or institutions to promote certain activities deemed beneficial.

Higher-Valued Uses

The allocation of resources or goods to their most profitable or beneficial applications, typically where they contribute the most to welfare or profitability.

Lower-Valued Uses

Activities or allocations of resources that do not maximize potential value or returns compared to other uses.