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a guest Feb 25th, 2019 196 Never
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  1.     import graph;
  2.    
  3.     // parameters to tweak
  4.    
  5.     real start = 0;
  6.     real end = 2;
  7.    
  8.     real graphleft = -1;
  9.     real graphright = 3;
  10.    
  11.     real f(real x) {
  12.         return x * x;
  13.     }
  14.    
  15.     real fderiv(real x) {
  16.         return 2 * x;
  17.     }
  18.    
  19.     real jumpsize = 1;
  20.    
  21.     real pointradius = 0.05;
  22.    
  23.     // stuff that draws
  24.     real jumps = (end - start) / jumpsize;
  25.    
  26.     path g = graph(f, graphleft, graphright);
  27.     draw(g, blue);
  28.    
  29.     real height = f(start);
  30.     for (int n = 0; n < jumps; ++n) {
  31.         pair p1 = (start + jumpsize * n, height);
  32.        
  33.         real x2 = start + jumpsize * (n+1);
  34.         real y2 = height + fderiv(x2) * jumpsize;
  35.         pair p2 = (x2, y2);
  36.        
  37.         draw(p1 -- p2, red);
  38.         height = y2;
  39.     }
  40.    
  41.     // draw points afterwards so they aren't covered by segments
  42.     height = f(start);
  43.     for (int n = 0; n <= jumps; ++n) {
  44.         real x = start + jumpsize * n;
  45.        
  46.             pair p = (x, height);
  47.             height = height + fderiv(x + jumpsize) * jumpsize;
  48.             pair p_actual = (x, f(x));
  49.            
  50.             draw(p -- p_actual, dashed);
  51.             fill(circle(p, pointradius), purple);
  52.             fill(circle(p_actual, pointradius), green);
  53.     }
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