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Green cubic curve depends on parameter p. Red curve is its derivative. Pink line has ordinate rico = -1. Therefore, intersection points A and B are those where red derivative = -1. Point C and D have same abscissas as A and B respectively. Therefore the blue tangents to green curve in C and D have always inclination -1 by construction. Do we always have two blue tangents? Maybe, or maybe not. It depends on parameter p. Explore the situation of the blue tangents by changing the value of p.