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) = (2x − 6y) i + (−6x + 10y − 9) j\

is conservative if we can find a scalar function such that . This is equivalent to solving the system of PDEs,

Integrate both sides of the first PDF with respect to :

where is some function independent of . Then differentiatng with respect to , we have

and so is indeed conservative, with

the answer is d

for problems like this theres an app, its photomath that explains the problem and gives the answer hope i