From 516e25958db812634be6c56be07397690e401fba Mon Sep 17 00:00:00 2001
From: Didnelpsun <48906416+Didnelpsun@users.noreply.github.com>
Date: Fri, 12 Feb 2021 00:14:02 +0800
Subject: [PATCH] Update
 differential-mean-value-theorem-and-applications-of-derivatives.tex

---
 ...tial-mean-value-theorem-and-applications-of-derivatives.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/advanced-math/knowledge/3-differential-mean-value-theorem-and-applications-of-derivatives/differential-mean-value-theorem-and-applications-of-derivatives.tex b/advanced-math/knowledge/3-differential-mean-value-theorem-and-applications-of-derivatives/differential-mean-value-theorem-and-applications-of-derivatives.tex
index dc0686c..7865e16 100644
--- a/advanced-math/knowledge/3-differential-mean-value-theorem-and-applications-of-derivatives/differential-mean-value-theorem-and-applications-of-derivatives.tex
+++ b/advanced-math/knowledge/3-differential-mean-value-theorem-and-applications-of-derivatives/differential-mean-value-theorem-and-applications-of-derivatives.tex
@@ -520,7 +520,7 @@ $\forall x\in U(x_0,\delta)$恒有$f(x)\leqslant f(x_0)$，则$f(x)$在$x_0$取
     \item 若参数方程下：$x=\phi(t),y=\psi(t)$，$\rm{d}s=\sqrt{\left(\dfrac{\rm{d}x}{\rm{d}t}\right)^2+\left(\dfrac{\rm{d}y}{\rm{d}t}\right)^2}\rm{d}t$\medskip\\$=\sqrt{\psi'^2(t)+\phi'^2(t)}\rm{d}t$，即$\rm{d}s=\sqrt{\psi'^2(t)+\phi'^2(t)}\rm{d}t$。
 \end{itemize}
 
-\subsection{曲率与曲率半径}
+\subsection{曲率}
 
 曲率\textcolor{violet}{\textbf{定义：}}表明曲线在某一点的弯曲程度的数值，针对曲线上某个点的切线方向角对弧长的转动率，通过微分来定义，表明曲线偏离直线的程度。曲率越大，表示曲线的弯曲程度越大。
 
@@ -590,6 +590,7 @@ $\therefore\dfrac{\rm{d}\alpha}{\rm{d}x}=\dfrac{y''}{1+y'^2}\Rightarrow\rm{d}\al
 
 $\therefore k=\left\lvert\dfrac{\rm{d}\alpha}{\rm{d}s}\right\rvert=\dfrac{\vert y''\vert}{(1+y'^2)^{\frac{3}{2}}}$。
 
+\subsection{曲率半径}
 
 \begin{minipage}{0.5\linewidth}
     $\bigcirc O$为函数$L$在点$X$处的曲率圆，该圆与$L$在$X$处相切，切线为$T$。