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) = 5y2z3 i + 10xyz3 j + 15xy2z2 k

If there is some scalar function such that as given, then this satisfies the following partial differential equations:

Integrate the first PDE with respect to :

Differentiate with respect to :

Differentiate with respect to :

So is indeed conservative.

14 x 10 5

step-by-step explanation:

10 5 = 100,000

14x10,000 = 140,000