Show that if the vector field f = pi + qj + rk is conservative and p, q, r have continuous first-order partial derivatives, then the following is true. ∂p ∂y = ∂q ∂x ∂p ∂z = ∂r ∂x ∂q ∂z = ∂r ∂y . since f is conservative, there exists a function f such that f = ∇f, that is, p, q, and r are defined as follows. (enter your answers in the form fx, fy, fz.) p = q = r = since p, q, and r have continuous first order partial derivatives, says that ∂p/∂y = fxy = fyx = ∂q/∂x, ∂p/∂z = fxz = fzx = ∂r/∂x, and ∂q/∂z = fyz = fzy = ∂r/∂y.