1. Explain why there are no points on the graph in the third quadrant. That is, based on the equation x^(2)y+xy^(2)=1, explain why the graph contains the points that it does. Explanations can begin with a phrase like "As x increases..." or "As y increases"
2. There is a point at which there is a horizontal tangent line. Find its coordinates.
3. Based on symmetry, state the coordinates of the point at which there is a vertical tangent line. Then give a brief algebraic justification of your answer. You do not need to numerically find the coordinates, just show the algebraic equation that must hold and point out the symmetry to the horizontal tangent case.