input courbes.mp;
%===========================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                0.2*(t**2)+0.5
enddef;

%=============================================================================
verbatimtex 
%&latex 
\documentclass{article} 
\usepackage{palatino} 
\newcommand{\vect}[1]{\overrightarrow{#1}}
\newcommand{\Vect}[1]{\overrightarrow{\strut #1}}
\begin{document} 
etex 
                
beginfig(1);
path p;
repere(0,0,-3,6,-1,8,1cm,1cm);
quad_x(1);
quad_y(1);
r_axes;
r_origine;
r_unites;
p = f_courbe(-3,6,100);
pickup pencircle scaled 1pt;
draw p withcolor blue;
pickup pencircle scaled 0.5pt;
tracef_tangente(1.2,5);
r_point_proj(1.2,fy(1.2));
r_point_proj(4.5,fy(4.5));
z0=f_point(1.2);
z1=r_point(4.3,4.55);
draw r_droitedir(1.2,fy(1.2),1.14);
label.top(btex $A$ etex, z0);
label.top(btex $M$ etex, z1);
label.bot(btex $a$ etex, r_point(1.2,0));
label.bot(btex $a+h$ etex, r_point(4.5,0));
label.lft(btex $f(a)$ etex, r_point(0,fy(1.2)));
label.lft(btex $f(a+h)$ etex, r_point(0,fy(4.5)));
label.top(btex $\mathcal{C}_f$ etex, r_point(5.2,6.5));
label.bot(btex $T$ etex, r_point(-2.5,-0.5));
%r_labelxy;
r_fin;
endfig;


beginfig(2);			   
path p;
picture approx;
repere(0,0,-3,6,-1,8,1cm,1cm);
quad_x(1);
quad_y(1);
r_axes;
r_origine;
r_unites;
p = f_courbe(-3,6,100);
pickup pencircle scaled 1pt;
draw p withcolor blue;
pickup pencircle scaled 0.5pt;
tracef_tangente(1.2,5);
r_point_proj(1.2,fy(1.2));
r_point_proj(4.5,fy(4.5));
z0=f_point(1.2);
z1=r_point(4.3,4.55);
z2=r_point(4.3,2.372);
r_point_proj(4.5,2.372);
label.top(btex $A$ etex, z0);
label.top(btex $M$ etex, z1);
label.top(btex $P$ etex, z2);
label.bot(btex $a$ etex, r_point(1.2,0));
label.bot(btex $a+h$ etex, r_point(4.5,0));
label.lft(btex $f(a)$ etex, r_point(0,fy(1.2)));
label.lft(btex $f(a+h)$ etex, r_point(0,fy(4.5)));
approx = thelabel.lft(btex $f'(a)h+f(a)$ etex, r_point(0,2.372));
unfill bbox approx ; draw approx;
label.top(btex $\mathcal{C}_f$ etex, r_point(5.5,5.2));
label.bot(btex $T$ etex, r_point(-2.5,-0.5));
%r_labelxy;
r_fin;
endfig;


beginfig(3);
path p;
picture approx ;
repere(0,0,-3,6,-1,8,1cm,1cm);
quad_x(1);
quad_y(1);
r_axes;
r_origine;
r_unites;
p = f_courbe(-3,6,100);
pickup pencircle scaled 1pt;
draw p withcolor blue;
pickup pencircle scaled 0.5pt;
tracef_tangente(1.2,5);
r_point_proj(1.2,fy(1.2));
r_point_proj(4.5,fy(4.5));
z0=f_point(1.2);
z1=r_point(4.3,4.55);
z2=r_point(4.3,2.372);
r_point_proj(4.5,2.372);
label.top(btex $A$ etex, z0);
label.top(btex $M$ etex, z1);
label.top(btex $P$ etex, z2);
label.bot(btex $a$ etex, r_point(1.2,0));
label.bot(btex $x$ etex, r_point(4.5,0));
label.lft(btex $f(a)$ etex, r_point(0,fy(1.2)));
label.lft(btex $f(x)$ etex, r_point(0,fy(4.5)));
approx = thelabel.lft(btex $f'(a)(x-a)+f(a)$ etex, r_point(0,2.372));
unfill bbox approx ; draw approx;
label.top(btex $\mathcal{C}_f$ etex, r_point(5.5,5.2));
label.bot(btex $T$ etex, r_point(-2.5,-0.5));
%r_labelxy;
r_fin;
endfig;

end