Generating the function from given coordinates and slopes

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To generate a function from given coordinates and slopes, one can either use manual mathematical procedures or software tools. A polynomial function may be appropriate, but without knowing the specific type of function, it’s challenging to ensure accuracy for other points. The discussion highlights that while a linear approximation (y=mx) was attempted, it does not fully capture the curve's behavior. Excel's curve fitting function is mentioned as a potential software solution for this task. Ultimately, identifying the correct function type is crucial for achieving accurate results.
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hi fellas, i have been given a graph from which i can extract the coordinates and the slopes but all i need is to generate the function this graph represents. can you suggest me any manual procedure to do this mathematically or do i have to use software to generate polynomial functions?
if there is any useful software to generate functions from co ordinates please let me know
 
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Do you have any ideas, suspicions etc as to what sort of function it is - polynomial, trigonometric, exponential...
Without that one could work out a function that fits the values and slopes but it wouldn't necessarily produce correct values for other points.
 
i got the curve to be sort of a straight line. I might have worked out with it to get a y=mx curve, but i m looking for a more accurate function because my straight line is slightly deviating from its path, not exponential though..actually i need to know if there is any mathematical manual process to get the accurate function or if you can suggest me a software which does it?
 
Excel has a curve fitting function.
 

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