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三次函数的零点问题是函数零点问题的常见问题,挖掘有关三次函数零点理论有助于快速、准确地求解相关问题.下面就三次函数零点存在的条件做一推理和题例应用.一、三次函数零点存在的条件设关于x的三次函数为f(x)=ax2+bx2+cx+d(这里取a<0),其定义域为R,f(x)的导函数为f′(x)=3ax2+2bx+c,该导函数是一个二次函数,其判别式为Δ=4b2-12ac=4(b2-3ac).
The zero point of the cubic function is a common problem of the zero point of the function, and excavating the zero point theory of the cubic function helps to solve the related problems quickly and accurately. The reasoning and application of the problem of the zero point of the cubic function are given below. The zero-point existence condition Let the cubic function of x be f (x) = ax2 + bx2 + cx + d (here a <0), the domain of which is defined as R and the derivative function of f = 3ax2 + 2bx + c, the derivative is a quadratic function, the discriminant is Δ = 4b2-12ac = 4 (b2-3ac).