Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each oth
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F is conservative if we can find a scalar funciton <em>f</em> such that grad(<em>f</em>) = F.
This would entail
Integrate both sides of the first equation with respect to <em>x</em> :
Differentiate both sides with respect to <em>y</em> :
Differentiate both sides with respect to <em>z</em> :
So we have
that satisfies
and so F is indeed conservative.