% (find-LATEX "2024-1-C3-pontos-criticos.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2024-1-C3-pontos-criticos.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2024-1-C3-pontos-criticos.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2024-1-C3-pontos-criticos.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2024-1-C3-pontos-criticos.pdf"))
% (defun e () (interactive) (find-LATEX "2024-1-C3-pontos-criticos.tex"))
% (defun o () (interactive) (find-LATEX "2024-1-C3-pontos-criticos.tex"))
% (defun u () (interactive) (find-latex-upload-links "2024-1-C3-pontos-criticos"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2024-1-C3-pontos-criticos.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2024-1-C3-pontos-criticos")
% (find-pdf-page   "~/LATEX/2024-1-C3-pontos-criticos.pdf")
% (find-sh0 "cp -v  ~/LATEX/2024-1-C3-pontos-criticos.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2024-1-C3-pontos-criticos.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2024-1-C3-pontos-criticos.pdf")
%   file:///home/edrx/LATEX/2024-1-C3-pontos-criticos.pdf
%               file:///tmp/2024-1-C3-pontos-criticos.pdf
%           file:///tmp/pen/2024-1-C3-pontos-criticos.pdf
%  http://anggtwu.net/LATEX/2024-1-C3-pontos-criticos.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps   "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2024-1-C3-pontos-criticos" "3" "c2m241pc" "c3pc")

% «.defs»		(to "defs")
% «.defs-T-and-B»	(to "defs-T-and-B")
% «.defs-caepro»	(to "defs-caepro")
% «.defs-pict2e»	(to "defs-pict2e")
% «.defs-maxima»	(to "defs-maxima")
% «.defs-V»		(to "defs-V")
% «.title»		(to "title")
% «.links»		(to "links")
% «.stewart-p856-ex10»	(to "stewart-p856-ex10")



\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\drafturl{http://anggtwu.net/LATEX/2024-1-C3.pdf}
\def\drafturl{http://anggtwu.net/2024.1-C3.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2024-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2024-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

% «defs-T-and-B»  (to ".defs-T-and-B")
\long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B       (#1 pts){\ColorDarkOrange{\bf(#1 pts)}}

% «defs-caepro»  (to ".defs-caepro")
%L dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L dofile "Piecewise2.lua"           -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua"           -- (find-LATEX "Escadas1.lua")
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt

% «defs-maxima»  (to ".defs-maxima")
%L dofile "Maxima2.lua"              -- (find-angg "LUA/Maxima2.lua")
\pu

% «defs-V»  (to ".defs-V")
%L --- See: (find-angg "LUA/MiniV1.lua" "problem-with-V")
%L V = MiniV
%L v = V.fromab
\pu


%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m241pcp 1 "title")
% (c2m241pca   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 3 - 2024.1}

\bsk

Aula 20: exercícios sobre pontos críticos

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://anggtwu.net/2024.1-C3.html}

\end{center}

\newpage

% «links»  (to ".links")
% (c2m241pcp 2 "links")
% (c2m241pca   "links")

{\bf Links}

\scalebox{0.6}{\def\colwidth{14cm}\firstcol{

\par \Ca{StewPtCap14p55} (p.841) O vetor gradiente
\par \Ca{StewPtCap14p65} (p.851) Teste da segunda derivada
\par \Ca{StewPtCap14p70} (p.856) 14.7 Exercícios (vamos fazer o 10)
\ssk
\par \Ca{3fT85} 2022.2: P1, gabarito da questão 2

\bsk

% (find-es "maxima" "2024.1-stewart-p856-ex10")
% (find-angg "MAXIMA/myqdraw1.mac")

{\footnotesize
\par \url{http://anggtwu.net/e/maxima.e.html\#2024.1-stewart-p856-ex10}
\par \url{http://anggtwu.net/MAXIMA/myqdraw1.mac.html}
\par \texttt{(find-es "maxima" "2024.1-stewart-p856-ex10")}
\par \texttt{(find-angg "MAXIMA/myqdraw1.mac")}
\par
}


}\anothercol{
}}

\newpage

% «stewart-p856-ex10»  (to ".stewart-p856-ex10")
% (find-es "maxima"  "2024.1-stewart-p856-ex10")
% (c2m241pcp 3 "stewart-p856-ex10")
% (c2m241pca   "stewart-p856-ex10")

{\bf Stewart, p.856, exercício 10}

%M (%i1) F   : x*y * (1-x*y);
%M (%o1) x\,y\,\left(1-x\,y\right)
%M (%i2) F   : x*y * (1-x-y);
%M (%o2) x\,\left(-y-x+1\right)\,y
%M (%i3) Fx  : diff(F, x);
%M (%o3) \left(-y-x+1\right)\,y-x\,y
%M (%i4) Fy  : diff(F, y);
%M (%o4) x\,\left(-y-x+1\right)-x\,y
%M (%i5) Fxx : diff(Fx, x);
%M (%o5) -\left(2\,y\right)
%M (%i6) Fxy : diff(Fx, y);
%M (%o6) -\left(2\,y\right)-2\,x+1
%M (%i7) Fyy : diff(Fy, y);
%M (%o7) -\left(2\,x\right)
%L maximahead:sa("xy(1-x-y)", "")
\pu

%M (%i8) [xmin,ymin,xmax,ymax] : [-2,-2,2,2];
%M (%o8) \left[ -2 , -2 , 2 , 2 \right] 
%M (%i9) mylevel(eq,[opts]) :=
%M   apply('imp1, append([eq, x,xmin,xmax, y,ymin,ymax], opts))$
%M (%i10) myQdraw("Stewart-p856-exerc10-F",     "height=2.5cm",
%M         mylevel(F=0,    lk("F=0"),    lc(orange)),
%M         mylevel(F=0.2,  lk("F=0.2"),  lc(red)),
%M         mylevel(F=-0.2, lk("F=-0.2"), lc(forest_green))
%M        );
%M (%o10) \includegraphics[height=2.5cm]{2024-1-C3/Stewart-p856-exerc10-F.pdf}
%M (%i11) myQdraw("Stewart-p856-exerc10-Fx-Fy", "height=2.5cm",
%M         mylevel(Fx=0,   lk("Fx=0"),   lc(red)),
%M         mylevel(Fy=0,   lk("Fy=0"),   lc(orange))
%M        );
%M (%o11) \includegraphics[height=2.5cm]{2024-1-C3/Stewart-p856-exerc10-Fx-Fy.pdf}
%L maximahead:sa("xy(1-x-y) 2", "")
\pu

%M (%i12) pontoscriticos : solve([Fx=0, Fy=0], [x,y]);
%M (%o12) \left[ \left[ x=0 , y=0 \right]  , \left[ x=0 , y=1 \right]  , \left[ x=1 , y=0 \right]  , \left[ x={\frac{1}{3}} , y={\frac{1}{3}} \right]  \right] 
%M (%i13) [P1,P2,P3,P4] : pontoscriticos;
%M (%o13) \left[ \left[ x=0 , y=0 \right]  , \left[ x=0 , y=1 \right]  , \left[ x=1 , y=0 \right]  , \left[ x={\frac{1}{3}} , y={\frac{1}{3}} \right]  \right] 
%M (%i14) at([Fxx,Fxy,Fyy], P1);
%M (%o14) \left[ 0 , 1 , 0 \right] 
%M (%i15) at([Fxx,Fxy,Fyy], P2);
%M (%o15) \left[ -2 , -1 , 0 \right] 
%M (%i16) at([Fxx,Fxy,Fyy], P3);
%M (%o16) \left[ 0 , -1 , -2 \right] 
%M (%i17) at([Fxx,Fxy,Fyy], P4);
%M (%o17) \left[ -\left({\frac{2}{3}}\right) , -\left({\frac{1}{3}}\right) , -\left({\frac{2}{3}}\right) \right] 
%M (%i18) 
%L maximahead:sa("xy(1-x-y) 3", "")
\pu

\scalebox{0.45}{\def\colwidth{8cm}\firstcol{

\vspace*{0cm}

\def\hboxthreewidth {10cm}
\ga{xy(1-x-y)}

}\def\colwidth{9cm}\anothercol{

\vspace*{0cm}

\def\hboxthreewidth {14cm}
\ga{xy(1-x-y) 2}

}}


\newpage


\scalebox{0.6}{\def\colwidth{9cm}\firstcol{

\def\hboxthreewidth {14cm}
\ga{xy(1-x-y) 3}

}\anothercol{
}}






\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}



% Local Variables:
% coding: utf-8-unix
% ee-tla: "c3pc"
% ee-tla: "c2m241pc"
% End:
