中值定理毕业论文中期报告

PickThe mid-value theorems is a series of mean value theorems in general, is a powerful tool research function. It includes luol theorem, Lagrange theorem and cauchy theorem, Taylor theorem. The mid-value theorems is the core of differential calculus theorem, the important tool of function, attention. Over the past few decades, people in real field on differential mid-value theorem on a lot of research. This paper mainly introduces several different methods to prove the mid-value theorem, at the same time the mid-value theorem is applied in the mathematical theory, such as the application and mathematical : value theorem, proof, application, mathematical modeling

构造函数有点“随缘”性，没有一个固定的步骤告诉你怎么构造函数的。只有靠平时多做多练才能比较熟练地构造函数。有专门的论文写关于如何构造大部分情况下的构造函数方法，我这里没法全贴出来。像e^x,sinx,lnx比较常见。本题中，[a,b]=[2,4]f(a)=1，f(b)=4要让构造出来的F(a)=F(b)，其实论证的结果也给了一些提示，就是分母中含有未知数xf'(x)=2f(x)/xf'(x)-2f(x)/x=0[xf'(x)-2f(x)]/x=0同乘x[x²f'(x)-2xf(x)]/x²=0x²f'(x)-2xf(x)=0明显是[x²f(x)]'=0但是x²f(x)明显不满足F(a)=F(b)又因为f(a)=1,f(b)=4设G(x)=x²f(x)G(a)=1²*1G(b)=4²*4所以在分母上尝试乘以x或者x²或者x³或者x^4，这个就靠经验来构造了。没有特定的一个方法。