Find the Equation of the Tangent Plane To $x ^ { 2 } + 2 x y + 4 y + 6 = z ^ { 2 }$

question 56

Multiple Choice

Find the equation of the tangent plane to $x ^ { 2 } + 2 x y + 4 y + 6 = z ^ { 2 }$ at the point (-4, 1, 3) .

• A) \(6 x + 4 y + 6 z = - 4\)
• B) \(- 6 x + 4 y + 6 z = - 2\)
• C) \(6 x - 4 y + 6 z = - 2\)
• D) \(6 x + 4 y + 6 z = 2\)
• E) \(6 x + 4 y + 6 z = - 2\)

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Definitions:

Excess Demand

A situation in an economic market where the quantity demanded of a product exceeds the quantity supplied at the current price.

Good Increases

A situation where the supply, quality, or availability of beneficial or valuable products or commodities rises.

Quantity Supplied

The amount of a product that producers are willing and able to sell at a given price over a specified period.

Product Price

The amount of money required to purchase a good or service, often determined by factors such as cost of production, market demand, and competition.