Math Problem Statement
The Terrain of a certain area follows the function f(x,y,z)= x^2+3xy +2z .If you are a the point (2,0,-1) , what is the change in the terrain if you begin to walk in the direction specified by the vector 2i + j - 2k
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Directional Derivatives
Gradient Vectors
Formulas
Directional derivative formula: D_uf = ∇f ⋅ u
Gradient of f: ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Unit vector: u = d / |d|
Theorems
Gradient Theorem for directional derivatives
Suitable Grade Level
Undergraduate Calculus (Grade 12+)
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