本文介绍经过三次函数图象上一点作切线,何时可作一条,何时可作两条,并说明它的应用,供读者参考.定理:经过三次函数f(x)=ax3+bx2+cx+d(a≠0)图象上的一点P(x0,f(x0))作切线,则(1)当3ax0+b=0时,只能作一条切线,该切线斜率k=f′(x0);(2)当3ax0+b≠0时,可作两条切线,两条切线斜率分别为k=f′(x0)和k=f′(-x02-b2a). This article describes the tangency of a point on the image of a cubic function, when it can be used as a tangent, and when it can be used as two, and explains its application for readers’ reference. Theorem: After a cubic function f(x)=ax3+bx2+cx A point P(x0,f(x0)) on a +d(a≠0) image is tangent. (1) When 3ax0+b=0, only one tangent line can be made. The slope of this tangent line is k=f’ ( X0); (2) When 3ax0+b≠0, two tangents can be made, and the slopes of the two tangents are k=f’(x0) and k=f’(-x02-b2a), respectively.