Solve the Problem $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$

question 207

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$ at the point $( 3,4 )$ in the direction in which the function decreases most rapidly.

• A) \(- 3 \sqrt { 26 }\)
• B) \(- \sqrt { 221 }\)
• C) \(- \sqrt { 173 }\)
• D) \(- \sqrt { 167 }\)

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Definitions:

Structured Programming

A programming paradigm aimed at improving the clarity, quality, and development time of a computer program by making extensive use of subroutines, block structures, and loops.

Adaptor Pattern

A software design pattern that allows interfaces of incompatible classes to work together by wrapping them in an adapter class.

Underlying Class

The actual implementation class of an object, especially in the context where the object is accessed through an interface or superclass.

Inheritance Diagram

A visual representation of the relationships between parent and child classes in object-oriented programming.