# How to find maximum/minimum on a locus object?

Magnus2Pi shared this question 4 years ago

Hi,

This curve, which is the locus of the angle alpha (scaled) as the point F varies on the x-axis.

Can GeoGebra give the maximum/minimum of this curve?

1

With First(<locus>,Length(<locus>)) you can create a list with all points of a locus

To select the points see attachment

1

Thanks!

I try to make a function from the list Function(First(<locus>,Length(<locus>))), but that leads to function undefined.

Any idea why?

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I see that the definition of function requires a special list in its constructor. Your max/min approach is fine.

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I dont see how to extract max and min from the list, though.

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Min = Element(Sort(Lok1P1, y(Lok1P1)), 1)

y(Lok1P1) --> only the y-values of the points

Sort(<list1>,<list2>) --> sort list2 then sort list1 in the sequence of list2

Element(<pointList>, 1) --> take the first Point from pointList

this Point has the lowest Y-value because the order is by the Y-value and NOT by the X-value

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Max is similar but: only points right from Min (see Lok1P2) because left from Min the Y-value is about 25 but this is not the Max. (zoom the graphic, then you can see the points left from Min with Y-value about 25)

The point with the highest Y-value in the sorted list Lok1P2 is the last. Length(<list>) give this index.

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as function (calculate 3 sides with Pythagoras and angle with this calculated 3 sides)

(without locus)

Note: GGB-Bug in Min/Max and Corner (when shift graphic to left and right)

1

you can use

f(x) = atan2d(y(A), x(A) - x) - atan2d(y(B), x(B) - x)

then max and min

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I dont see what this function has to do with the problem of measuring the angle beta as B varies along x-axix.

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Nice!

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I supposed in your first post that C varies along x-axix

you can delete alpha in attached

Files: foro.ggb
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Nice!

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and then solve f'(x) = 0 with CAS :

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That is a decent solution.

However, what i really miss in this is the ability to give a Locus-object as a input to the constructor for a function object. (The function becomes either a parametric curve (x(t),y(t)) or a function y=f(x)).

Anyone interested in extending GeoGebra with this functionality?