diff --git a/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.pdf b/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.pdf
index 1627a5d..bffc60a 100644
Binary files a/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.pdf and b/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.pdf differ
diff --git a/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.tex b/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.tex
index a3dc635..ec5654a 100644
--- a/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.tex
+++ b/advanced-math/exercise/6-differential-calculus-of-multivariate-functions/differential-calculus-of-multivariate-functions.tex
@@ -194,6 +194,10 @@ $\therefore\lim\limits_{(x,y)\to(0,0)}f(x,y)-f(0,0)=bx+cy+o(\rho)$。
 
 又$x+y+z+xyz=0$对$x$求导：$1+z_x'+yz+xyz_x'=0$，代入$(0,1,-1)$，$1+z_x'-1=0$，$z_x'=0$。代入$f_x'(x,y,z)=e^0=1$。
 
+\section{多元函数极值最值}
+
+\subsection{无条件极值}
+
 \section{多元函数微分应用}
 
 \subsection{空间曲线的切线与法平面}