Determine whether or not f is a conservative vector field. if it is, find a function f such that f = ∇f. if it is not, enter none. f(x, y) = (2x − 4y) i + (−4x + 10y − 9) j

is conservative if



It's clear that this is true, since both partial derivatives reduce to -4, so is indeed a conservative vector field.

Since is conservative, there must be some scalar function such that




Integrating with respect to yields



and differentiating with respect to yields





Thus the scalar potential of is



where is an arbitrary constant.