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新教材中导数的介入,为研究函数的性质提供了新的活力。利用导数研究函数的单调区间、极值、最值等已成为高考命题的一个新热点,其中多项式函数中一元三次函数是考查的重点,近几年全国各地的高考对此都有考查。基于导数在一元三次函数中的重要地位,我们有必要通过它来研究函数f(x)=ax3+bx2+cx+d(a>0,a,b,c,d为常数)的性质。一、利用导数来研究三次函数的单调性三次函数的导函数f′(x)=3ax2+2bx+c(a=0),
The intervention of derivatives in the new textbook provides new vitality for the study of the nature of the function. Monotonous intervals, extremums, and maxima of the functions have become a new hot spot in the college entrance examination test. The one and three times polynomial functions in the polynomial functions are the key points of the test. In recent years, the college entrance examination has been examined in all parts of the country. Based on the important position of the derivative in the univariate function, it is necessary for us to study the properties of the function f (x) = ax3 + bx2 + cx + d (a> 0, a, b, c and d are constants) First, the derivative function is used to study the derivative function f ’(x) = 3ax2 + 2bx + c (a = 0) of the monotonicity cubic function of the cubic function.