Determine whether $\mathbf { F }$ is conservative. If so, find a function $f$ such that $\mathbf { F } = \nabla f$.
$$\mathbf { F } ( x , y , z ) = 4 x ^ { 3 } y ^ { 2 } z ^ { 3 } \mathbf { i } + 2 x ^ { 4 } y z ^ { 3 } \mathbf { j } + 3 x ^ { 4 } y ^ { 2 } z ^ { 2 } \mathbf { k }$$

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The Answer is

f ( x , y , z ) = x ^ { 4 } y ^ { 2 } z ^ { 3 } + C

Determine Whether F\mathbf { F }F Is Conservative fff Such That F=∇f\mathbf { F } = \nabla fF=∇f

Determine Whether $\mathbf { F }$ Is Conservative $f$ Such That $\mathbf { F } = \nabla f$