Tangent Line and Equation of Tangent

The idea of a tangent is something you already know from geometry — a line that just touches a circle at one point. In calculus, we extend that idea to any smooth curve: the tangent line at a point is the straight line that best approximates the curve near that point. Its slope is given by the derivative $\frac{dy}{dx}$ evaluated at the point of contact. Once you have that slope, writing the equation of the tangent is j …