Abstract: Derivative is the research tool most commonly used for solving tangent of curve. By use of the relationship between “equivalent roots” and tangent of curves, a concrete approach to solve problems concerning tangent of curve is put forth. Also introduced in the article was the concept of curve tangent and the basic idea of using “equivalent roots of an equation to depict tangent of curve. And the necessary and sufficient conditions when a straight line is tangent with a cubic functional picture are also worked out.