What can you say about the graph of a solution of the equation y' =
x
y
3
36
when x is close to 0? What if x is large?

If x is close to 0, then y' =
x
y
3
36
is (choices are: large, close to 0, and close to 36) , and hence y' is (choices are: large, close to 0, and close to 36) Thus, the graph of y must have a tangent line that is nearly (choices are: horizontal, vertical). If x is large, then
x
y
3
36
is (choices are: large, close to 0, and close to 36), and the graph of y must have a tangent line that is nearly (choices are: horizontal, vertical). (In both cases, we assume reasonable values for y.)