Wiki-Quellcode von Lösung Analysis
Zuletzt geändert von akukin am 2025/12/29 16:38
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| author | version | line-number | content |
|---|---|---|---|
| 1 | {{detail summary="Erwartungshorizont"}} | ||
| 2 | <p> | ||
| 3 | {{formula}} f^{\prime}(x)=3x^{2}+6x=3x(x+2)=0 \Leftrightarrow x_{1}=-2 \lor x_{2}=0 {{/formula}} | ||
| 4 | </p><p> | ||
| 5 | {{formula}} f^{\prime\prime}(x)=6x+6=0 \Leftrightarrow x_{3}=-1 {{/formula}} (Nullstelle von {{formula}} f^{\prime\prime} {{/formula}} mit Vorzeichenwechsel) | ||
| 6 | </p> | ||
| 7 | {{formula}} | ||
| 8 | f^{\prime\prime}(-2)=-6 < 0, f(-2)=4 \Rightarrow H(-2|4) {{/formula}} | ||
| 9 | <br> | ||
| 10 | {{formula}} | ||
| 11 | f^{\prime\prime}(0)=6 > 0, f(0)=0 \Rightarrow T(0|0) | ||
| 12 | {{/formula}} | ||
| 13 | <br> | ||
| 14 | {{formula}} f^{\prime}(-1)=-3 \Rightarrow {{/formula}} Steigung {{formula}} -3 {{/formula}} im Wendepunkt. | ||
| 15 | {{/detail}} | ||
| 16 | |||
| 17 | |||
| 18 | {{detail summary="Erläuterung der Lösung"}} | ||
| 19 | |||
| 20 | {{/detail}} |