Math Problem Statement

Find the unit vector in the direction for which the directional derivative of f(x,y)=squarer root of (7x^3y^3−7xy^2) at the point (−1,−1) is a maximum.

Submit a unit vector using exact values. Make sure to enter an answer for each of the response fields

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Directional Derivatives
Gradient
Partial Derivatives

Formulas

Directional derivative formula: D_u f = ∇f ⋅ u
Gradient: ∇f = (∂f/∂x, ∂f/∂y)
Partial derivatives for function f(x, y)

Theorems

Gradient Theorem: The directional derivative is maximized in the direction of the gradient vector.

Suitable Grade Level

Grades 11-12, Undergraduate