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## Derivative of regression line

I have used a regression line to find a curve fitting my datapoints.
Now I want to know the lowest point on my curve and I am trying to find that by finding the point where the derivative of the regression line is 0.

So I made a formula g(a) using the results from the regress function (by refering to entries in the regress solution matrix). I can use this function correctly to plot the curve and to calculate results for different values of a.

However when I want to get the derivative it gives me a formula including the regress function. Solving the derivative for 0 is impossible.

To check if I use the correct functions I also made a formula h(a). Basically the same as g(a), but now I have manually typed the results from the regress function in the formula, instead of linking to the regress solution matrix.

Now I can get the derivative and solve for equal to 0.

However this is not convenient if my datapoints change, because I have to manually update h(a) each time.

Is what I want possible and how to solve this? In other words, what am I doing wrong?

Attached a mathcad 15 file with an example.

1 ACCEPTED SOLUTION

Accepted Solutions
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## Re: Derivative of regression line

Incidentally, If all your polynomes are 3rd order and like the one given, the (positive) zero always occurs at

And instead of symbolically solving this, you could also use a numeric solver, which can happily work with the output of the interp function:

Success!
Luc

7 REPLIES 7
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Hi

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Try this

then:

Success!
Luc

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## Re: Derivative of regression line

If you look at the error message it says the result is too big to display.  However, you can still use the result.

Alan

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## Re: Derivative of regression line

Incidentally, If all your polynomes are 3rd order and like the one given, the (positive) zero always occurs at

And instead of symbolically solving this, you could also use a numeric solver, which can happily work with the output of the interp function:

Success!
Luc

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## Re: Derivative of regression line

Rather than "regress" you might try "polyfit."  Polyfit returns a function so you don't have to extract the coefficients from a vector.

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## Re: Derivative of regression line

Hello !,

you simply have to reset the symbolic variables

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