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今天小编为大家带来的是好学高数（五）：微分的中值定理。

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Dear you, this is LearningYard.

Today&39;s edition brings you the Mean Value Theorem of Differential.

中值定理

一、罗尔定理

（1）f(x)在闭区间[a ,b]上连续；

（2）f(x)在开区间(a,b) 内可导；

（3）f(x)在区间端点的函数值相等，即f(a)=f(b) ，

那么在(a,b) 内至少有一点ξ (a<ξ<b)，使得函数f(x) 在该点的导数等于零，即f&39;(ξ)=0。

（可用来证明唯一性）

1、 Rolle&39;s theorem

(1) f (x) is continuous on the closed interval [a, b];

(2) F (x) is derivable in the open interval (a, b);

(3) The function values of f (x) at the end of the interval are equal, that is, f (a)=f (b), so there is at least one point in (a, b) ξ (a< ξ< b) , so that the derivative of function f (x) at this point is equal to zero, that is, f &39;（ ξ)= 0 (can be used to prove uniqueness)

二、拉格朗日中值定理

三、柯西中值定理（参数方程）

洛必达法则

适用对象：0比0型、无穷比无穷型

当遇到无穷*0型，将其中一个乘数转化为分母，再进行求导。

Applicable objects: 0 to 0 type, infinite to infinite type When encountering infinite * 0 type, convert one of the multipliers to the denominator, and then take the derivative.

泰勒公式

（做题时使用频率小）

(Less frequently used in questions)

END

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审核：闫庆红