Charakteristische Punkte einer Funktion PDF

Summary

This document presents a graph of a cubic function with its key points marked, such as maximum points, minimum points, inflection points, and intercepts. It also provides the corresponding function formula f(x) = (1/10) * x³ - x² + 2x + 4. The document is suitable for undergraduate-level mathematics study.

Full Transcript

## Charakteristische Punkte der Funktion ### Graph einer kubischen Funktion The image displays a graph of a cubic function. The graph has been annotated to show various details. * **Hochpunkt:** *Die Funktion wechselt vom Steigen zum Fallen.* The function switches from increasing to decreasin...

## Charakteristische Punkte der Funktion ### Graph einer kubischen Funktion The image displays a graph of a cubic function. The graph has been annotated to show various details. * **Hochpunkt:** *Die Funktion wechselt vom Steigen zum Fallen.* The function switches from increasing to decreasing at the maximum point. * **Wendepunkt:** *Die Funktion wechselt ihre Krümmung. Hier: Wechsel von Rechts- zu Linkskrümmung.* The function switches its curvature at the inflection point. Here, it is shown switching from convex to concave. * **Schnittpunkt mit der y-Achse:** The point at which the function intersects with the y-axis. * **Nullstelle:** *Schnittpunkt mit der x-Achse.* The function's x-intercept, where it intersects the x-axis. * **Tiefpunkt:** *Die Funktion wechselt vom Fallen zum Steigen.* The function switches from decreasing to increasing at the minimum point. ### Function Formula The box below the graph displays the function formula for the graphical representation: f(x) = (1/10) * x³ - x² + 2x + 4

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