Math Problem Statement
Find an equation of the tangent plane to the given surface at the specified point. z = 4(x − 1)2 + 3(y + 3)2 + 5, (2, −1, 21)
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Partial Derivatives
Tangent Planes
Surface Geometry
Formulas
Tangent Plane Equation: z - z0 = fx(x - x0) + fy(y - y0)
Partial Derivatives: fx = ∂z/∂x, fy = ∂z/∂y
Theorems
Tangent Plane Theorem
Suitable Grade Level
University Level (Calculus III or equivalent)
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