input courbes.mp;

vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                sqrt(t-2)
enddef;
%=========================================================================    
beginfig(1);    
path p; 
repere(0,0,-1,9,-1,3,1cm,1cm);
r_axes;
r_origine;
r_unites;
pickup pencircle scaled 1.5pt;
p = f_courbe(fx,fy,2,9,100);
draw p;% withcolor blue ;
pickup pencircle scaled 0.5pt;
label.top(btex $y=\sqrt{x-2}$ etex, r_point(7,1));
r_ppoint(2,fy(2));
drawarrow r_point(2,0)--r_point(2,2);
draw r_droitedir(2,0,fy(2.5));
r_ppoint(2.5,fy(2.5));
draw r_droitedir(2,0,fy(3));
r_ppoint(3,fy(3));
draw r_droitedir(2,0,fy(4));
r_ppoint(4,fy(4));
label.lrt(btex $A(a;f(a))$ etex, r_point(2,fy(2)));
r_labelxy;
r_fin;
endfig;

%=========================================================================
vardef gx(expr t) =
t
enddef;
vardef gy(expr t) =
                       1/t+1
enddef;
%==========================================================================
vardef fx(expr t) =
t
enddef;
vardef fy(expr t) =
                       t**2+1
enddef;
%==========================================================================

beginfig(2);   
path p,q; 
repere(0,0,-2,7,-3,5,1cm,0.5cm);
r_axes;
r_origine;
pickup pencircle scaled 1pt;
p = f_courbe(fx,fy,-2,1,100);
q = f_courbe(gx,gy,1,7,100);
draw p; draw q;
pickup pencircle scaled 0.5pt;
r_ppoint(fx(1),fy(1));
drawarrow f_point(fx,fy,1)--f_point(fx,fy,1)-0.8*(1*_ux,(fy_derive(fy,1,0.1))/(fx_derive(fx,1,0.1))*_uy);
drawarrow f_point(gx,gy,1)-- f_point(gx,gy,1)+1*(1*_ux,(fy_derive(gy,1,0.1))/(fx_derive(gx,1,0.1))*_uy);
label.top(btex $A(a;f(a))$ etex, r_point(1,fy(1)));
endfig;


end