script that checks if two function have an intersections point?

Mads Frederik Toft shared this question 5 months ago
Needs Answer

I have piecewise function and have made geogebra write it as two functions f and g with respect to to their domains.

Sequence 1 tests whether their exists a point where

f(x)=g(x)

Sequence 2 tests whether if their derivatives are different for all points in their domain.

What I would like to do is make a script which can take both sequences and test them on two functions, and then return the point from sequence 1 (if it exists).

And for sequence two either return the text (The function f-g is smooth) if their derivatives don't equal. Or if the is a point where the derivates equal either show this point of their tangents in this points.


My first attempt of problem 1

if(Sekvens(f(j) ≟ g(j), 1, 1), f(t))


Problem here is that it works for one specific function and not for all.


So any idears/thoughts? :)

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