Hi, guys:

Here is a formula



And the Targets are:
1. Draw the plot, but only the first quadrant is required.
2. Find the value of fn when M is maximum.
3. Find the maximum value of M.

I did the 1st target successfully, but can not find the values of fn and M. I have tried my best and search the forum but could not find any way to fix it. Please help to fix it, Thank you very much!

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LLC.sm (12 KiB) downloaded 44 time(s).

Wrote

Wrote

Please help to fix it, Thank you very much!

You need the Golden ratio ... doctored version.
If the function is a data set, spline/smooth the region
... as well the FindIndex is a good utility.
Cheers ... Jean

LLC Doctored for MAX.sm (27 KiB) downloaded 38 time(s).
Golden ratio QUICK Copy.sm (123 KiB) downloaded 38 time(s).

wow!I think I understand, it is very useful, thank you very much!

The built-in functions are perfectly well suited for the purpose. You just need to separate differentiation from root finding.


LLC.sm (11 KiB) downloaded 46 time(s).

... refreshed version.
Cheers ... Jean

Golden Search Copy.sm (23 KiB) downloaded 35 time(s).

Here is your functions peak point solved with various solvers.

Regards

LLC1.sm (9 KiB) downloaded 46 time(s).

Wrote

2. Find the value of fn when M is maximum.
3. Find the maximum value of M.

It all depend upon the accuracy you want.
Smath was not even ½ pregnant that roots existed from libraries.
Cheers ... Jean

Apart from Findroot() there are other functions in Nonlinear Solvers to.
Check that plugins page in Reference Book, there may some info you can use.

Regards

LLC1.sm (13 KiB) downloaded 44 time(s).