Math Problem Statement
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y, z) = 7x + 9y z , (3, 7, −1) maximum rate of change
direction vector
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Multivariable Calculus
Gradient
Partial Derivatives
Formulas
Gradient formula: ∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Magnitude of a vector: |∇f| = √((∂f/∂x)^2 + (∂f/∂y)^2 + (∂f/∂z)^2)
Unit vector formula: u = ∇f / |∇f|
Theorems
Gradient Theorem
Suitable Grade Level
Undergraduate Calculus
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