import graph;

size(10cm,0);

real[] xpt={-1,.5,2,2.5,4};
real[] ypt={2,-1,2,-2,3};

real xmin=min(xpt)-.5,xmax=max(xpt)+.5;
real ymin=min(ypt)-.5,ymax=max(ypt)+.5;

marker croix=marker(scale(2)*rotate(45)*cross(4),1bp+red);

draw(graph(xpt,ypt,Hermite(monotonic)),croix);

void tanghoriz(int k,real lg=1,real ld=lg, pen p=dashed, arrowbar arr=None) {
  draw(((xpt[k]-lg,ypt[k]))--((xpt[k]+ld,ypt[k])),p,arr);
}

tanghoriz(1,lg=1.5,p=.5bp+red,Arrows(SimpleHead));
tanghoriz(2);

xaxis(Label("$x$",position=EndPoint, align=NE),
  xmin=xmin,xmax=xmax,
  Ticks(scale(.7)*Label(align=E),
  NoZero,
  Step=1,step=.25,Size=1mm, size=.5mm,
  pTick=black,ptick=gray),
  Arrow);
yaxis(Label("$y$",position=EndPoint, align=NE),
  ymin=ymin,ymax=ymax,
  Ticks(scale(.7)*Label(),
  NoZero,
  Step=1,step=.25,Size=1mm, size=.5mm,
  pTick=black,ptick=gray),
  Arrow);