Question

calc iii - potential function

Answer 1

\(\mathbf F = \langle y + 4 z, x + z, 4x + y\rangle = \mathbf \nabla \phi\)

\(\phi_x = y + 4z \implies \phi = xy + 4xz + \alpha(y,z)\)

\(\phi_y = x+z \implies \phi = xy + y
z + \beta(x,z)\)

\(\phi_z = 4x + y \implies \phi = 4xz + yz + \gamma(x,y)\)

Looks like: \(\phi = \underbrace{xy}_{\gamma} + \underbrace{4xz}_{\beta} + \underbrace{yz}_{\alpha} + C\)

Answer 2

thank you C: