(a) What can you say about the graph of a solution of the equation y* = - when x is close to 0? What if x is large?
If x is close to 0, then y^3 is nearly vertical (V) - (In both cases, we assume reasonable values for y.) When x is large, the graph of y must have a tangent line that is nearly horizontal.
We substitute the values of y and y and test the solution to see if the left-hand side (LHS) is equal to the right-hand side (RHS):
LHS: y = 4(c - x^2)^(1/2)
RHS: y^3 = [4(c - x^2)^(-1/2)]^3 = (c - x^2)^(3/2)
RHS = LHS