Question

Determine if the given vector field \vec{F} is conservative or not.\\ \vec{F} = (-3y, 12y^2 - 3z^2 - 3x - 3z, -6yz - 3y)\\ conservative\\not conservative\\ If \vec{F} is conservative, find all potential functions $f$ for \vec{F} so that \vec{F} = \nabla f. (If \vec{F} is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)\\f(x, y, z) =

          Determine if the given vector field \vec{F} is conservative or not.\\
\vec{F} = (-3y, 12y^2 - 3z^2 - 3x - 3z, -6yz - 3y)\\
conservative\\not conservative\\
If \vec{F} is conservative, find all potential functions $f$ for \vec{F} so that \vec{F} = \nabla f. (If \vec{F} is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)\\f(x, y, z) =

Determine if the given vector field F⃗ is conservative or not.

F⃗ = (-3y, 12y^2 - 3z^2 - 3x - 3z, -6yz - 3y)

conservative
not conservative

If F⃗ is conservative, find all potential functions f for F⃗ so that F⃗ = ∇f. (If F⃗ is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)
f(x, y, z) =

Added by Santiago W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

12/15/2022

Step 1

Step 1: A vector field $\vec{F} = (P, Q, R)$ is conservative if and only if $\nabla \times \vec{F} = \vec{0}$. Show more…

Show all steps

Thanks for your feedback!

Determine if the given vector field $\vec{F}$ is conservative or not. $\vec{F} = (-3y, 12y^2 - 3z^2 - 3x - 3z, -6yz - 3y)$ conservative not conservative If $\vec{F}$ is conservative, find all potential functions $f$ for $\vec{F}$ so that $\vec{F} = \nabla f$. (If $\vec{F}$ is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.) $f(x, y, z) = $