From 60c44453550c265b1f3b785c08a1e003c73426cc Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Sat, 21 Sep 2024 16:09:01 +0200 Subject: [PATCH] Nullstellen und Extrempunkte von Funktionsscharen --- klausurx.typ | 15 +++++++++++++++ pdfs/klausurx.pdf | Bin 184325 -> 187094 bytes 2 files changed, 15 insertions(+) diff --git a/klausurx.typ b/klausurx.typ index b9624c2..9ab5ca3 100644 --- a/klausurx.typ +++ b/klausurx.typ @@ -54,3 +54,18 @@ Das heißt das wir das $x$ des Punktes einsetzen mussten und das $y$ des Punktes b) Berechnen Sie die Koordinaten des Tiefpunktes der Graphen von $f_a$ in Abhängigkeit von $a$. +$ +f_a (x)&=x^2-2a x +8a -16\ +f'_a (x)&=2x-2a\ +f''_a (x)&=2\ \ +0&=2x-2a &&|:2\ +0&=x-a &&|-a\ +a&=x +$ +Da $f''(a)=2>0$ ist handelt es sich um einen #text(weight: "bold", [Tiefpunkt]).\ +Es gilt also#footnote([Hier wurde $x$ durch $a$ ersetzt]): +$ +f(a)&=a^2-2a^2+8a-16\ +&=-a^2+8a-16 +$ +Also T($a$|$-a^2+8a-16$), hier ist $x=a$ und $f(a)=y$. \ No newline at end of file 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