平面曲线的切线问题有许多实际来源,例如作圆周运动的物体在任意时刻的运动方向,就是圆在该点处的切线方向;又如在设计光学透镜时,必须知道光线射入透镜的角度以便应用反射定律,重要的角是光线与镜片截面曲线的法线之间的夹角,而法线与切线垂直,即问题也归结为求曲线的切线;另 There are many practical sources for the tangent problem of planar curves. For example, the direction of motion of an object moving in a circular motion at any time is the tangential direction of the circle at that point. Also, when designing an optical lens, the angle of light entering the lens must be known so that Using the law of reflection, the important angle is the angle between the ray and the normal to the section curve of the lens, and the normal is perpendicular to the tangent, that is, the problem is also attributed to the tangent to the curve;