In fact, the most important question is how to determine that two curves at a common point will merge at such an "acute angle". I just don't know how to call it mathematically correct, so I use this term. I have attached a graph of three curves, of which the yellow and blue curve form an "acute angle", and the yellow and green do not form such an "angle". In fact, the angle between the tangents at a common point is 0 for both cases. But is there a way to determine without looking at the graph that the yellow curve "transitions" to the green one "smoothly", and to the blue one with a "peak". The equations of the curves: the blue curve: ,
\[Alpha] = {1072 - 173.64999999999964` v - 1053.510000000002` v^2 -
4794.608388545948` v^3 + 10250.579098091992` v^4 -
4882.862709546044` v^5, -2579 + 367.7999999999993` v +
1085.800000000003` v^2 + 1474.5933742968045` v^3 -
4803.408260125245` v^4 + 2456.944885828447` v^5,
9.88383` + 643.53585` v - 560.0617000000002` v^2 -
604.8447774764995` v^3 + 817.3174429750306` v^4 -
192.31364549852992` v^5}
, the yellow curve:
[Beta] = {417.948- 578.4099999999996 v -
243.95000000000118v^2 + 393.08600000000206 v^3 -
296.9425000000008v^4 + 121.26850000000013 v^5, -1997.27+
259.14999999999964 v + 1303.1000000000022v^2 - 2037.5 v^3 +
1427.8500000000058v^4 - 475.4899999999998 v^5,
113.517+ 125.37 v + 476.27v^2 - 2032.92 v^3 +
1893.0629999999996v^4 - 652.1182 v^5}
, the green curve :
[Gamma] = {1072 - 173.64999999999964v - 1053.510000000002 v^2 +
2103.8958575598153v^3 - 3136.883524725092 v^4 +
1606.0956671652757v^5, -2579 + 367.7999999999993 v +
1085.800000000003v^2 - 794.1323873673391 v^3 -
449.44909006839225v^4 + 371.7114774357324 v^5,
9.88383+ 643.53585 v - 560.0617000000002v^2 -
1808.5353536247153 v^3 + 3135.9297882918345v^4 -
1307.2354146671187 v^5}
.I apologize in advance for the abundance of quotation marks and my own terms.
