Hey, ist es irrelevant, wie hoch/tief ich einen Extrempunkt oder Wendepunkt skizziere (von f‘(x) zu f(x))?
Hey, ist dies irrelevant, wenn ich jetzt die erste Ableitungsfunktion gegeben habe und nun zu der Ausgangsfunktion (f(x)) aufheizen möchte? Nur wenn ich ja nun dann für die Nullstellen von f‘(x) die Extrempunkte in f(x) einzeichnen möchte, dann weis ich ja nicht, wie hoch oder tief er ist (genau so bei den Wendepunkten)? Ist dies irrelevant wie hoch oder tief oder wie funktioniert dies?
Vielen Dank.
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If only f’ is given, f is not fully determined due to the constants. So if you are to draw a root function to f’, you may choose a constant value, e.g. 0, and then you must record the extremes for your constant.
Yes, but the function is not given and one only sees the graph of the derivation function f’(x) and should now perform the output function f(x) (sketch)? What does it look like?
Just as I wrote it
Okay, thank you. How do I calculate exactly the position of the extreme points?
This depends on the question. If you are to reconstruct the function profile from the course of the derivation, that is actually irrelevant. Why? Because the so-called absolute member (i.e. the coefficient which does not carry x) falls away during the derivation. Consequently, from the course of the derivation, nothing can be said about the displacement of the original function along the y-axis.
Example: The functions f(x)=x2 and g(x)=x2+4 both have the derivative f'(x)=g'(x)=2x. Both have their extreme value at x=0. But at f(x), this is at y=0, at g(x) at y=4.
Okay, thank you. I am concerned, however, with the so-called lead, how does it look?
You just have to read what I wrote, so to speak “backward”. I have only explained WARUM that the displacement along the x axis cannot be reproduced from the derivation. That’s exactly how it explained @Maxi170703.
Okay, thanks for your help.
jep.
Okay, so it’s clear to me how high or deep I’m entering the extreme, mainly the X-value is right? Is that right?
You can read the x values of the extreme points from the derivation graph, but not the y values.
Okay, do you mean that you can’t read it out of the derivation graph on your own, where exactly the extremes of the output function are located and you can decide exactly for this reason how high/low the extreme is then? Did I get it right?
Because it’s just a sketch, I think it’s irrelevant. Unless you previously calculated Extrema, turning points, etc. But if you are to draw the exact course of the graph and it is not a sketch, then it plays a role.
Go to school yourself and if the speech is of a sketch, you don’t have to calculate anything and you’re just saying that Extrema in the derivation are turning points of the initial function (reduction) etc., then you really just have to sketch the rough course.