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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'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'(ξ)=0。
（可用来证明唯一性）
1、 Rolle'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 '（ 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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文案&排版:易春秀
审核：闫庆红
