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:

Neutron

A subatomic particle that contributes mass to a nucleus and is electrically neutral.

Electron

A stable, subatomic particle with a negative charge.

Earth's Crust

The outermost layer of the Earth, consisting of solid rocks and minerals, divided into the oceanic and continental crusts.

Oceanic Crust

The thin layer of Earth's crust that underlies the ocean basins, composed mainly of basalt and denser than continental crust.