common tangent of two curves I need simple code
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I need the slope of common tangent given in the figure below. Actually I need the coordinates of common tangent touching points to each curve. It seems easy for the curves below but I have very different and difficult curves and I need to find very accurately.
I need the slope of the tangent and I need the equation of tangent line if possible. I can do it analytically but I need a simple code to do it because I will do it for many curves.. I understand gradient or diff but the code I need must be for both numerical and symbolic. The problem is that if I have a very steep curve I may not have a good approximation with numerical methods. Is it possible with simple code?
Thanks,
best wishes,
4 comentarios
Adam Danz
el 25 de Oct. de 2019
Editada: Adam Danz
el 25 de Oct. de 2019
"it is not a math problem. "
"... the program code then compare these slopes and reports which x value these slopes are equal to each other."
I thought of 2 problems with this approach.
- There many be many points that have approximately the same slope between the two curves. For example, at the minima of the curves, the slopes are both 0.
- The slopes between the two curves will probably not exactly match. For example, at the two points in your image that share the same slope, one may be -0.499124 while the other is -0.498456.
Perhaps another idea would be to find the line that connects two interpolated points, one from each parabola, that has the lowest y-intercept. Or maybe, find the line that connects points from each parabola that contains no coordinates below the line.
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