BangBienthien
Forfatter:
Bùi Minh Quang
Sidst opdateret:
9 år siden
Licens:
Creative Commons CC BY 4.0
Resumé:
Đây là Bảng biến thiên
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
Đây là Bảng biến thiên
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
\documentclass[12pt,a4paper,oneside]{report}
%======= Packages=======
\usepackage[utf8]{vietnam}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{color}
\usepackage{exscale}
%\usepackage[notref,notcite] {showkeys}
\usepackage[mathscr]{eucal}
\usepackage{enumerate}
\usepackage{fancyhdr}
\usepackage[unicode]{hyperref}
\usepackage[top=35mm, bottom=30mm, left=35mm, right=20mm]{geometry}
\usepackage{tkz-tab}
\begin{document}
\begin{tikzpicture}
\tkzTabInit[lgt=3,espcl=1.5]%
{$x$ /1,
$x^2-3x+2$ /1,
$(x-e)\ln x$ /1,
$\dfrac{x^2-3x+2}{(x-e)\ln x}$ /2}
{$0$ , $1$ , $2$ , $e$ ,$+\infty$}
\tkzTabLine{ t,+,z,-,z,+,t,+,}
\tkzTabLine{ d,+,z,-,t,-,z,+,}
\tkzTabLine{ d,+,d,+,z,-,d,+,}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[nocadre]
{$x$ /.7, $y'$ /.7,$y$ /2}
{$-\infty$ ,$-1$ , $+\infty$}
\tkzTabLine{ ,-,d,-, }
\tkzTabVar{ - / $2$ ,+D- / $+\infty$/ $-\infty$ , + / $2$ }
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[lgt=1.2,espcl=5]
{$x$ /1.2, $f’(x)$ /1.2,$f(x)$ /2.5}
{$-\infty$ , $\dfrac{1}{2}$ , $+\infty$}
\tkzTabLine{,-,d,-,}
\tkzTabVar{+/$-\dfrac{1}{2}$ ,-D+/$-\infty$/$+\infty$, -/$-\dfrac{1}{2}$}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[lgt=1.2,espcl=3]
{$x$ /1.2, $f’(x)$ /1.2,$f(x)$ /2.5}
{$-\infty$ , $-\sqrt{2}$,$0$,$\sqrt{2}$, $+\infty$}
\tkzTabLine{,-,z,+,z,-,z,+,}
\tkzTabVar{+/$+\infty$ ,-/$-3$, +/$1$,-/$-3$,+/$+\infty$}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[]
{$u$ /1.2, $f’(u)$ /1.2,$f(u)$ /2.5}
{,$-\dfrac{1}{4}$ , $\dfrac{-1+\sqrt{3}}{2}$ , $+\infty$,}
\tkzTabLine{t,h,d,+,z,-,d,h,t}
\tkzTabVar{LD/,-/$-\dfrac{5}{8}$ ,+/$\dfrac{2-\sqrt{3}}{2}$, -/$-\infty$,}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[lgt=3]%
{$t$/1,%
$f’(t)$ /1,%
$f(t)$ /2}%
{$-\infty$ , $-\frac{2}{3}$ , $\frac{1}{3}$ , $+\infty$}%
\tkzTabLine{ ,-, 0 ,+, 0 ,-, }
\tkzTabVar %
{
+/$0$,-/$-6$ ,+/$3$,-/$0$
}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[nocadre]
{$x$ /.7, $y'$ /.7,$y$ /2}
{$\frac 12$ ,$\frac 94$ , $4$}
\tkzTabLine{ d,+,0,-,d }
\tkzTabVar{ - / $\sqrt{14}$ ,+/$2\sqrt{7}$ , - / $\sqrt{14}$ }
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[nocadre]
{$t$/1,$f'(t)$/1,$f(t)$/2}
{$0$,$\frac12$,$+\infty$}
\tkzTabLine{,-,0,+,}
\tkzTabVar{+/$+\infty$,-/ $\frac34$/,+/$+\infty$}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$ /1, $f(x)$ /2}
{$-\infty$ , $-\dfrac{2}{3}$ , $\dfrac{1}{3}$ , $+\infty$}
\tkzTabLine{ ,-, 0 ,+, 0 ,-, }
\tkzTabVar {+/$0$,-/$-6$ ,+/$3$,-/$0$}
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tikzset{h style/.style = {pattern=north west lines}}
\tkzTabInit[nocadre,lgt=2,espcl=3]
{$x$ /1, $f'(x)$ /1,$f(x)$ /2}
{$0$,$3$,$+\infty$}
\tkzTabLine{ d ,+ ,z,-, }
\tkzTabVar{D-/ $-\infty$ , +/ $ \frac{2}{9}$, -/ $0$ / }
\end{tikzpicture}
\vspace{1cm}
\begin{tikzpicture}
\tikzset{h style/.style = {pattern=north west lines}}
\tkzTabInit[nocadre,lgt=2,espcl=3]{$x$ /1, $f'(x)$ /1,$f(x)$ /2}{
$-\infty$,$-2$,$2$,$+\infty$}%
\tkzTabLine{ ,-, d ,h,d ,+, }
\tkzTabVar{+/ $1$ / , -DH/ $-3$ / , D-/ $-5$, +/ $1$ / }
\end{tikzpicture}
\vspace{1cm}
\begin{center}
\textbf{{\Large BANG BIEN THIEN CUA CAC HAM SO THUONG GAP O TRUONG THPT}}
\end{center}
\section{Hàm số bậc hai $\mathbf{y=ax^2+bx+c}$}
\subsection{ Trường hợp $\mathbf{a<0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/1}{$-\infty$,$x_0$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/1}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,+,0,-,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,+,0,-,}
\tkzTabVar{-/ $-\infty$,+/ $y_0$/,-/ $-\infty$}
\end{tikzpicture}
\subsection{ Trường hợp $\mathbf{a>0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/1}{$-\infty$,$x_0$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/1}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,-,0,+,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,-,0,+,}
\tkzTabVar{+/$+\infty$,-/ $y_0$/,+/$+\infty$}
\end{tikzpicture}
\section{Hàm số bậc ba $\mathbf{y=ax^3+bx^2+cx+d}$}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac <0}$ và $\mathbf{a<0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$, $+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$, $+\infty$}
\tkzTabLine{,-,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$, $+\infty$}
\tkzTabLine{,-,}
\tkzTabVar{+/ $+\infty$,-/ $-\infty$ }
\end{tikzpicture}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac <0}$ và $\mathbf{a>0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$+\infty$}
\tkzTabLine{,+,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre,espcl=6]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$, $+\infty$}
\tkzTabLine{,+,}
\tkzTabVar{-/ $-\infty$,+/ $+\infty$ }
\end{tikzpicture}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac =0}$ và $\mathbf{a>0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,+,0,+,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,+,0,+,}
\tkzTabVar{-/ $-\infty$, R/,+/ $+\infty$ }
\end{tikzpicture}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac =0}$ và $\mathbf{a<0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,-,0,-,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_0$,$+\infty$}
\tkzTabLine{,-,0,-,}
\tkzTabVar{+/ $+\infty$, R/,-/ $-\infty$ }
\end{tikzpicture}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac >0}$ và $\mathbf{a>0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\tkzTabLine{,+,0,-,0,+,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\tkzTabLine{,+,0,-,0,+,}
\tkzTabVar{-/ $-\infty$, +/ $y_1$,-/ $y_2$, +/ $+\infty$ }
\end{tikzpicture}
\subsection{Trường hợp $\mathbf{\Delta=b^2-3ac >0}$ và $\mathbf{a<0}$}
\textbf{Bước 1:}Khởi tạo.\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\end{tikzpicture}\bigskip
\textbf{Bước 2: }Thêm dấu của đạo hàm:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\tkzTabLine{,-,0,+,0,-,}
\end{tikzpicture}
\bigskip
\textbf{Bước 3: }Thêm chiều biến thiên:\bigskip
\begin{tikzpicture}
\tkzTabInit[nocadre]{$x$/1,$f'(x)$/1,$f(x)$/2}{$-\infty$,$x_1$,$x_2$,$+\infty$}
\tkzTabLine{,-,0,+,0,-,}
\tkzTabVar{+/ $+\infty$, -/$y_1$,+/ $y_2$, -/$-\infty$ }
\end{tikzpicture}
\end{document}