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第八周。

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2022-11-06 19:06:06 +08:00
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03函数的导数.tex
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@@ -554,7 +554,7 @@ Leibniz记号：记$\Delta f = f(x_0 + \delx) - f(x_0)$，那么
\begin{proof}
注意$x_1 < x < x_2$，可以将$x$表示为
\[x = \lambda x_1 + 1 - \lambda x_2 = \frac{x_2 - x}{x_2 - x_1}x_1 + \frac{x - x_1}{x_2 - x_2}x_2\]
\[x = \lambda x_1 + (1 - \lambda) x_2 = \frac{x_2 - x}{x_2 - x_1}x_1 + \frac{x - x_1}{x_2 - x_2}x_2\]
利用下凸的性质
\[f(x) \leq \frac{x_2 - x}{x_2 - x_1}f(x_1) + \frac{x - x_1}{x_2 - x_2}f(x_2)\]
@@ -643,7 +643,7 @@ Leibniz记号：记$\Delta f = f(x_0 + \delx) - f(x_0)$，那么
曲线作图步骤：对于方程$y = f(x)$，
\begin{enumerate}
\item 确定函数$f$的定义域
\item 检查$f$对对称性：奇偶性与周期性
\item 检查$f$的对称性：奇偶性与周期性
\item 检查曲线的渐近线：垂直、水平斜渐近线
\item 研究导函数$\deriv{f}$：确定函数的增减区间、极值点、临界点
\item 研究二阶到函数$f^{\prime \prime}$：确定曲线的上下凸区间与拐点