power(x,n)=x**n 
F(x,y)=power(x,2) - 3*x*y  +  power(y,2) + 10;
DF_x(x,y)= 2*x - 3*y;
DF_y(x,y)= 2*y - 3*x;
delta = 0.00001;
g2(x) = -sqrt(x + 4); dg2(x)=(g2(x+delta)-g2(x))/delta; 
a= -1;b=dg2(-1)*a;
set arrow from a,g2(a) to a+a,g2(a)+b;
set arrow from a,g2(a),F(a,g2(a)) to a+a,g2(a)+b, F( a+a,g2(a)+b); 
set xrange [-4:4] 
set pointsize 0.1 
splot F(x,y), "dados" with points;
print "Aperte enter para terminar" 
pause -2