AnalyzeImplicitFunction Applet
This is a primarily Applet under development.
Here follows some explanation to see it on work for the implicit given function y(x) by the equation y^3+x*y-6=0. Later on this will be 'variable'.
The aim is to see the three 'branches' of y(x).
Maybe you try to find the x value where the derivative approaches infinity, nearby x= -6.5.First steps using the applet
- Click on the button "press to start the computation" and the first computation will be done. The green graph represents the y^3+
0 *y-6 = f(y) and its zero is the solution needed.
Notice: the information in the upper panel! y'(0) is given too.- Drag the x slider a bit to the right and or left (say 1 and -1) and press each time after a change "next computation".
The graph of y will be displayed (though it is a linear interpolation of computed y(x) values).
Note The black line under the x-axis as well as the short vertical red line in its middle: The end points
of this 'interval' define the starting values of the ZeroFinder. If the corresponding y(x) values are not of different sign, no solution will be computed and NaN will be displayed as (new) y(x) value.
As a consequence you have to move this interval such, that the green line as a zero inbetween.- Move the x-slider now to several x-values and see the y(x) graph changing.
- Now we want to expand THIS graph of y(x) to -10.
You have to fill in a suitable value (finish with <enter>) say -9 in the input field in the upper right part of applet.
Now you can drag the x-slider to values around -9 ± 5 !
Note: move the black line to the right, such that the right zero of the green graph will be computed.
Maybe you zoom in/out to see the (magenta) graph y(x) at those very negative x values.- Now find a new branch of y(x)! Press "next branch". The green graph (at starting point x =0) will be displayed as a blue graph! The black line has to be moved more to the left side, take -3 , then press "next computation".
The blue graph gets green again, and if all is done as described the leftmost zero will be computed as first point of a new branch of y(x), which will become visible as you force a computation about say x = -7 . Visible after zoom out!Now you may experiment for yourself to compute the third branch ;-) .
Use the input value and the sliders ...