Consider the Surface Given By $z = x y ^ { 3 } - x ^ { 2 } y$

question 235

Essay

Consider the surface given by $z = x y ^ { 3 } - x ^ { 2 } y$ . Find an equation for the tangent plane to the surface at the point $( 3,2,6 )$ . Also, find parametric equations for the normal line to the surface at the point $( 3,2,6 )$

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Definitions:

Lava

Magma that is erupted onto the surface, or the rock mass into which it solidifies.

Uplift

The vertical elevation of the Earth's surface due to natural causes like tectonic movements.

Metamorphism

The mineralogical and structural changes of solid rock in response to changes in environmental conditions, especially at depth.

Solidification

The process in which magma cools and hardens into solid rock, with or without the formation of crystals.