Consider the differential equation $\dfrac{dy}{dx} = x^{4}(y-2)$.
(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.
(b) While the slope field in part (a) is drawn at only twelve points, it is defined at every point in the $xy$-plane. Describe all points in the $xy$-plane for which the slopes are negative.
(c) Find the particular solution $y = f(x)$ to the given differential equation with the initial condition $f(0) = 0$.