Sequence to find the extreme points of a function?

Mads Frederik Toft shared this question 3 years ago

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I have been trying to construct a sequnce which taken a function f(x) and for some integer j scans a set to find the extreme point value.

f(x) = 1 / 2 x³ - 2x² + 2

Sequence(If(f'(j) ≟ 0, j), j, -3, 3, 0.5)

How ever the main problem is that this sequence cannot find the extreme value if its a fraction.

So any surgestions on that I am missing will be welcomed ? :)

p.s. I know there is a build-in function in Geogebra to find the extreme values, but I would to ignore that if possible.

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Comments (4)

Simona Riva ● 3 years ago

I can't see a general solution, since each function you enter may have a different domain.

So you should create two different Sequence commands, one for each portion of the domain you want to scan, and Join them in a single list, for a nicer output. (you will need to avoid in the Sequence command the point/points/intervals in which your function is not defined)

I'd also consider to clean up a bit the resulting list, using RemoveUndefined command.

Try e.g. in your file

RemoveUndefined(Sequence(If(f'(j) ≟ 0, j), j, -3, 3, 0.5))

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Mads Frederik Toft ● 3 years ago

Thank you for your fine answer, and it does work. The main issue is still getting a way for the sequence to see all the extreme points and not only the whole numbers. But my issue is when you talk about a sequence to scan each part of the domain? How large a step do I use for each sequence?

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Michael Borcherds ● 3 years ago

Try

Solutions(f'(x))

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rami ● 3 years ago

The tip from Michael works fine for me.

But why not just Root() (for f'=0)?

Files: Solutions01.ggb

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