Find the Equation of the Tangent Plane to the Surface $3 x y z + x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 15$

question 32

Multiple Choice

Find the equation of the tangent plane to the surface $3 x y z + x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 15$ at (1, -3, 2) .

• A) \(- 15 x + 33 y + 3 z = - 108\)
• B) \(- 15 x + 33 y + 3 z = 108\)
• C) \(15 x + 33 y + 3 z = - 108\)
• D) \(- 15 x - 33 y + 3 z = - 108\)

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Definitions:

Assimilation

In psychology, a cognitive process where individuals integrate new information into existing cognitive schemas.

Accommodation

In psychology, the process of adjusting one's cognitive structures to incorporate new information.

Schema

A cognitive framework or concept that helps organize and interpret information, allowing individuals to make sense of their experiences and the world around them.

Jean Piaget

A Swiss psychologist known for his pioneering work in child development and his theory of cognitive development.