Determine Whether $\mathbf { F }$ Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

question 51

Multiple Choice

Determine whether $\mathbf { F }$ is conservative. If so, find a function $f$ such that $\mathbf { F } = \nabla f$ .
Select the correct answer.
$$\mathbf { F } ( x , y ) = \left( 5 x ^ { 4 } + 4 y \right) \mathbf { i } + \left( 7 x - 5 y ^ { 4 } \right) \mathbf { j }$$

• A) \(f ( x , y ) = 5 x ^ { 4 } + 4 y + 7 x - 5 y ^ { 4 } + C\)
• B) not conservative
• C) \(f ( x , y ) = x ^ { 5 } + y ^ { 5 } + C\)
• D) \(f ( x , y ) = x ^ { 5 } + 4 y ^ { 2 } + 7 x ^ { 2 } - y ^ { 5 } + C\) .

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Definitions:

High Risk

Indicates a situation or activity that involves a significant chance of loss, harm, or failure.

Reinforcing

Strengthening a behavior by providing a consequence that increases the likelihood of the behavior being repeated.

Construct System

A psychological framework used to understand and interpret the world, unique to each individual.

Range of Convenience

The scope or area within which a particular activity, concept, or object is considered appropriate, useful, or accessible.