文[1]对三次函数f(x)=ax3+bx2+cx+d对称中心的研究中,同时也涉及到了它的导函数f′(x)=3ax2+2bx+c的对称性.但是没有对一般的导函数与原函数的对称关系展开讨论,本文将对此展开进一步的探究.首先,我们来探究,原函数对称时,导函数的对称性如何?若函数f(x)关于x=a对称且可导,则f( In [1], the symmetry of the derivative function f ’(x) = 3ax2 + 2bx + c is also involved in the study of the center of symmetry of the cubic function f (x) = ax3 + bx2 + cx + d. First of all, let us explore the symmetry of the original function when the symmetry of the original function, if the function f (x) on the x = a symmetric and can guide, then f (