Math Problem Statement
The derivative of f (x, y, z) at a point P is greatest in the direction of Ai+jk. In this direction the value of the derivative is 2√3.
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Gradient
Directional Derivative
Vectors
Formulas
D_{\mathbf{u}} f = \nabla f \cdot \mathbf{u}
|\mathbf{A}| = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}
f_x + f_y + f_z = 6
Theorems
Gradient Theorem
Directional Derivative Formula
Suitable Grade Level
Undergraduate Calculus
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