Plotting local max-min-points ?

[lvl107]

  Hello Everyone.

  From :

       Plotting local max-min-points ?

           Thanks in advance.

                 Regards.

[terryhendicott]

Hi,

Set a function that is the derivative of f(x).

Use the root function on this derivative within a range to determine unique roots.

You now have enough info to plot the points.

[ValeryOchkov]

May be like thi

[lvl107]

Many thanks both of you, Valery. And I still have a query : "How to prove what point is local min-point ?

Best Regards.

[Werner_E]

[lvl107]

Could you attach *.xmcd ? ( I'm afraid I may hit wrong key stroke... )

    Best Regards. 

[Fred_Kohlhepp]

AWWW!  C'mon!

[Werner_E · Accepted solution]

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@lvl107 wrote:

Could you attach *.xmcd ? ( I'm afraid I may hit wrong key stroke... )

    Best Regards. 

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Hmm, really!??

Here's a slightly different approach:

Unfortunately the more direct and logical

does not work in Mathcad - muPad is not capable to find the solutions.

[Fred_Kohlhepp]

Some basic calculus (see Werner's application):

• First derivatives of a function are zero at inflection points (maxima/minima),
• The sign of the second derivative at the inflection point indicates minima (second derivative positive) or maxima (second derivative negative.)

[Werner_E]

In case of this function Mathcads symbolics is capable enough to give you al solutions, so you should use it.

If your goal is to limit the results to x1<x<x2 you may use the "assume" modifier.