Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne.) f(x, y, z) = 7y2z3 i + 14xyz3 j + 21xy2z2 k

Solution:

Given: F(x, y, z) = 7y²z³ i + 14xyz³ j + 21xy²z² k

F is a conservative field if curl F = 0, there exist a scalar potential function  such that F = .

curl f =

Thus,curl F is conservative.

To find f such that F = gradf.

Integrate the above terms with respect to x.

Hence, the scalar potential function is .

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.

for future students the answer is b

hope i

-lavira: )