Consider the differential equation $\dfrac{dy}{dx} = \dfrac{-xy^2}{2}$. Let $y = f(x)$ be the particular solution to this differential equation with the initial condition $f(-1) = 2$.
(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.
(b) Write an equation for the line tangent to the graph of $f$ at $x = -1$.
(c) Find the solution $y = f(x)$ to the given differential equation with the initial condition $f(-1) = 2$.