Consider the differential equation $\frac { d y } { d x } = \frac { - x y ^ { 2 } } { 2 }$. 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. (Note: Use the axes provided in the test booklet.) (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 $f ( - 1 ) = 2$.
Consider the differential equation $\frac { d y } { d x } = \frac { - x y ^ { 2 } } { 2 }$. 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.
(Note: Use the axes provided in the test booklet.)
(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 $f ( - 1 ) = 2$.