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Find the equation of the tangent plane to the surface determined by x^3 y^2 + z - 50 = 0 at x =...

Question:

Find the equation of the tangent plane to the surface determined by {eq}\ x^3 y^2 + z - 50 = 0 \ {/eq} at x = 3, y = 2.

z =

Tangent Plane to the Surface:

The tangent plane to a surface has as its normal vector the gradient of the surface. The gradient is computed as the vector containing the partial derivatives of the surface.

Answer and Explanation:

First, we solve for the missing variable, z. When {eq}x=3 {/eq} and {eq}y=2 {/eq} we have

{eq}x^3 y^2 + z - 50 = 0 \\ (3)^3 (2)^2 + z - 50 = 0...

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Tangent Plane to the Surface

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 3
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