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I am trying to construct a general function/method based on two sets of minimum/maximum data point constraints, which can take on new values in different situations. The only known data for this general function is the starting point (y-axis intercept) and the x-range. The rate of change over time must equal zero, so the amount increased/decreased must be compensated within the x-range. Optimally will vary as little as possible, as long as it meets the constraints.

I attached a figure of an example plot. The minimum constraint data points are marked as the 'necessary' function. The maximum constraint data points are marked as 'maximal.' The function marked as 'case 2' is an example of the general function that would satisfy the constraints.

I would appreciate any advice or suggestions on how to approach this problem as I've had very little success so far. Thank you in advance.

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# Regression Analysis - Constructing a Model ((Need Help Please))

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