Determine whether or not f is a conservative vector field. If it is, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne. ) f(x, y) = (y2 − 6x)i 2xyj
1 answer:
It looks like the vector field is
is conservative if we can find a scalar function whose gradient is . This entails solving the partial differential equations
Integrate both sides of the second PDE with respect to y :
Differentiate with respect to x and solve for :
It follows that is indeed conservative with potential function
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