$\"\"$

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The function is $\"\"$ .

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Definition of conservative :

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In a vector field $\"\"$ , if $\"\"$ then F is conservative.

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If F is conservative then the potential function for $\"\"$ is $\"\"$ .

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The function is $\"\"$ .

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$\"\"$

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$\"\"$

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So F is conservative.

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$\"\"$

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If F is conservative, then find the potential function for $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ equation (1)

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$\"\"$

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$\"\"$

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$\"\"$ equation (2)

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$\"\"$

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$\"\"$

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$\"\"$ equation (3)

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From equation (1), equation (2) and equation (3), $\"\"$ .

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$\"\"$

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F is conservative.

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The potential function is $\"\"$ .