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

question 83

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$ at the point $( 4,5 )$ in the direction in which the function increases most rapidly.

• A) \(\sqrt { 293 }\)
• B) \(3 \sqrt { 42 }\)
• C) \(\sqrt { 299 }\)
• D) \(\sqrt { 365 }\)

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Definitions:

Teaspoon (tsp)

A unit of measure typically used in cooking, equivalent to approximately 5 milliliters.

Equivalent Fractions

Fractions that have different numerators and denominators but represent the same value or proportion of a whole.

Proportions

The relationship in size, amount, or degree between different parts of a whole.

Body Surface Area

The total external surface area of the human body, important in determining dosages for medical treatments and assessing skin involvement.