documentclass[border=5pt,varwidth]{standalone}
usepackage{asymptote}

begin{document}

begin{asy}
settings.outformat="png";
// settings.render=10; //<<<----
settings.prc=false;

import graph3;
import contour;
size(7.5cm,0);
size3(7.5cm,IgnoreAspect);
currentprojection=orthographic(-6,-20,600);
currentlight=White;
limits((0,0,0),(10,10,300));
xaxis3(OutTicks(Step=2));
yaxis3(OutTicks(Step=5));
zaxis3(Bounds(Min,Max),InTicks(Step=100,Label(align=-X),NoZero));
real f(pair z) {return 2z.x^2-z.x+z.y^2;}
draw(surface(f,(0,0),(10,10),nx=10,Spline),lightgray,meshpen=black);
path p1=(5,1)--(9,1)--(9,4)--(5,4)--cycle,
     p2=(4,0)--(0,8),
     p3;
for(int i=0; i<=10;++i) p3=p3..point(p2,i/10);
guide[][] tabgui={{p1,p2,p3}};
draw(lift(f,tabgui),1bp+red);
draw(path3(p1),1bp+.8green);
draw(path3(p2),1bp+.8purple);
draw(extrude(p1,axis=200Z),blue+opacity(.75));
end{asy}

end{document}

documentclass[border=5pt,varwidth]{standalone}
usepackage{asymptote}

begin{document}

begin{asy}
settings.outformat="png";
settings.render=15;
settings.prc=false;

import graph3;
currentprojection=orthographic(1,-2,1);
currentlight=(1,-1,0.5);
size(7cm,0);
real f(pair z) {return abs(z)^2;}
path3 gradient(pair z) {
static real dx=sqrtEpsilon, dy=dx;
return O--((f(z+dx)-f(z-dx))/2dx,
(f(z+I*dy)-f(z-I*dy))/2dy,0);}
pair a=(-1,-1);
pair b=(1,1);
triple F(pair z) {return (z.x,z.y,0);}
add(vectorfield(gradient,F,a,b,red));
draw(surface(f,a,b,Spline),gray+opacity(0.5));
xaxis3(XY()*"$x$",OutTicks(XY()*Label));
yaxis3(XY()*"$y$",InTicks(YX()*Label));
zaxis3("$z$",OutTicks);
end{asy}

end{document}