Solve the Problem $\frac { 5 } { 88 } \sqrt { 2 }$

question 266

Multiple Choice

Solve the problem.
-Find the derivative of the function f(x, y, z) = ln(xy + yz + zx) at the point (8, 16, 24) in the direction in which the function increases most rapidly.

• A) \(\frac { 5 } { 88 } \sqrt { 2 }\)
• B) \(\frac { 5 } { 56 } \sqrt { 2 }\)
• C) \(\frac { 5 } { 104 } \sqrt { 2 }\)
• D) \(\frac { 5 } { 136 } \sqrt { 2 }\)

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Definitions:

Basic Steps

Basic Steps typically refer to the foundational or initial procedures in a process or methodology, outlining the essential phases needed to achieve a particular goal or complete a project.

Linear Optimization Model

A mathematical technique used to find the best outcome, such as maximum profit or lowest cost, in a model whose requirements are represented by linear relationships.

Outcomes

The possible results or consequences of a specific situation, experiment, or decision.

Reduced Cost

In linear programming, the amount by which the objective function coefficient of a variable must decrease before that variable's value increases in the optimal solution.