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 .

linear

step-by-step explanation:

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