Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Directional Derivative
Gradient of a Function
Unit Vector
Vector Calculus

Formulas

Directional derivative D_u f = ∇f ⋅ u
Magnitude of gradient |∇f(1,1,2)| = sqrt(3^2 + (-1)^2 + 5^2) = sqrt(35)
Max value of directional derivative: D_max = |∇f(1,1,2)|
Min value of directional derivative: D_min = -|∇f(1,1,2)|

Theorems

Gradient Theorem
Directional Derivative Formula

Suitable Grade Level

College Level or Advanced High School Calculus