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lehrkraefte:blc:miniaufgaben [2024/04/23 10:09] Ivo Blöchliger [29. April 2024 bis 3. Mai 2024] |
lehrkraefte:blc:miniaufgaben [2024/05/06 13:40] Ivo Blöchliger |
</PRELOAD> | </PRELOAD> |
| |
==== 22. April 2024 bis 26. April 2024 ==== | |
=== Dienstag 23. April 2024 === | ==== 6. Mai 2024 bis 10. Mai 2024 ==== |
Leiten Sie von Hand und ohne Unterlagen ab: | === Dienstag 7. Mai 2024 === |
<JS>miniAufgabe("#exonurpolynome","#solnurpolynome", | Mit Hilfe des TR, berechnen Sie die Nullstellen, Extremalstellenkandidaten und Wendestellenkandidaten. |
[["a) $f(x)=-\\frac{4}{3}x^{11}-\\frac{1}{9}x^{9}+\\frac{2}{3}x^{3}\\quad$ b) $f(x)=-\\frac{1}{2}x^{12}+\\frac{1}{5}x^{7}+\\frac{1}{2}x^{4}\\quad$ ", "a) $f'(x)=-\\frac{44}{3}x^{10}-x^{8}+2x^{2}\\quad$ b) $f'(x)=-6x^{11}+\\frac{7}{5}x^{6}+2x^{3}\\quad$ "], ["a) $f(x)=-\\frac{4}{3}x^{11}-\\frac{4}{9}x^{6}+\\frac{2}{9}x^{2}\\quad$ b) $f(x)=\\frac{1}{5}x^{12}-\\frac{1}{2}x^{7}+\\frac{4}{3}x^{5}\\quad$ ", "a) $f'(x)=-\\frac{44}{3}x^{10}-\\frac{8}{3}x^{5}+\\frac{4}{9}x\\quad$ b) $f'(x)=\\frac{12}{5}x^{11}-\\frac{7}{2}x^{6}+\\frac{20}{3}x^{4}\\quad$ "], ["a) $f(x)=-\\frac{1}{3}x^{11}-\\frac{1}{2}x^{10}+\\frac{1}{6}x^{5}\\quad$ b) $f(x)=-\\frac{2}{3}x^{11}-\\frac{2}{7}x^{9}+\\frac{2}{9}x^{8}\\quad$ ", "a) $f'(x)=-\\frac{11}{3}x^{10}-5x^{9}+\\frac{5}{6}x^{4}\\quad$ b) $f'(x)=-\\frac{22}{3}x^{10}-\\frac{18}{7}x^{8}+\\frac{16}{9}x^{7}\\quad$ "], ["a) $f(x)=-\\frac{1}{2}x^{9}+\\frac{1}{3}x^{5}-\\frac{3}{8}x^{2}\\quad$ b) $f(x)=-\\frac{4}{3}x^{12}-\\frac{3}{5}x^{11}-\\frac{4}{9}x^{4}\\quad$ ", "a) $f'(x)=-\\frac{9}{2}x^{8}+\\frac{5}{3}x^{4}-\\frac{3}{4}x\\quad$ b) $f'(x)=-16x^{11}-\\frac{33}{5}x^{10}-\\frac{16}{9}x^{3}\\quad$ "], ["a) $f(x)=\\frac{3}{5}x^{12}-\\frac{2}{3}x^{5}+\\frac{1}{4}x^{4}\\quad$ b) $f(x)=\\frac{3}{4}x^{9}-\\frac{3}{7}x^{5}-\\frac{2}{5}x^{2}\\quad$ ", "a) $f'(x)=\\frac{36}{5}x^{11}-\\frac{10}{3}x^{4}+x^{3}\\quad$ b) $f'(x)=\\frac{27}{4}x^{8}-\\frac{15}{7}x^{4}-\\frac{4}{5}x\\quad$ "], ["a) $f(x)=\\frac{2}{3}x^{12}+\\frac{3}{8}x^{8}+\\frac{4}{3}x^{7}\\quad$ b) $f(x)=-\\frac{1}{5}x^{12}-\\frac{1}{3}x^{6}-\\frac{1}{2}x^{3}\\quad$ ", "a) $f'(x)=8x^{11}+3x^{7}+\\frac{28}{3}x^{6}\\quad$ b) $f'(x)=-\\frac{12}{5}x^{11}-2x^{5}-\\frac{3}{2}x^{2}\\quad$ "], ["a) $f(x)=\\frac{1}{4}x^{12}-\\frac{1}{2}x^{10}-\\frac{2}{5}x^{7}\\quad$ b) $f(x)=-\\frac{1}{8}x^{12}-\\frac{1}{5}x^{5}-\\frac{3}{4}x^{4}\\quad$ ", "a) $f'(x)=3x^{11}-5x^{9}-\\frac{14}{5}x^{6}\\quad$ b) $f'(x)=-\\frac{3}{2}x^{11}-x^{4}-3x^{3}\\quad$ "], ["a) $f(x)=\\frac{3}{2}x^{12}-\\frac{2}{3}x^{10}+\\frac{1}{8}x^{3}\\quad$ b) $f(x)=\\frac{3}{4}x^{12}+\\frac{1}{3}x^{9}-\\frac{2}{5}x^{4}\\quad$ ", "a) $f'(x)=18x^{11}-\\frac{20}{3}x^{9}+\\frac{3}{8}x^{2}\\quad$ b) $f'(x)=9x^{11}+3x^{8}-\\frac{8}{5}x^{3}\\quad$ "], ["a) $f(x)=\\frac{4}{9}x^{12}+\\frac{4}{9}x^{6}-\\frac{3}{8}x^{3}\\quad$ b) $f(x)=\\frac{1}{3}x^{6}+\\frac{1}{4}x^{5}+\\frac{2}{3}x^{2}\\quad$ ", "a) $f'(x)=\\frac{16}{3}x^{11}+\\frac{8}{3}x^{5}-\\frac{9}{8}x^{2}\\quad$ b) $f'(x)=2x^{5}+\\frac{5}{4}x^{4}+\\frac{4}{3}x\\quad$ "], ["a) $f(x)=\\frac{1}{8}x^{10}-\\frac{2}{7}x^{8}-\\frac{4}{7}x^{3}\\quad$ b) $f(x)=\\frac{1}{3}x^{12}-\\frac{1}{5}x^{6}-\\frac{1}{2}x^{2}\\quad$ ", "a) $f'(x)=\\frac{5}{4}x^{9}-\\frac{16}{7}x^{7}-\\frac{12}{7}x^{2}\\quad$ b) $f'(x)=4x^{11}-\\frac{6}{5}x^{5}-x\\quad$ "]], | Machen Sie eine Tabelle mit diesen $x$-Werten sowie die zugehörigen $y$-Werte und Steigungen. |
" <br> "); | Für Extremalstellenkandidaten notieren Sie zusätzlich das Vorzeichen der zweiten Ableitung. |
| Skizzieren Sie dann mit diesen Informationen den Graphen. |
| <JS>miniAufgabe("#exokurvendiskussionMitTRquartic","#solkurvendiskussionMitTRquartic", |
| [["$f(x) = -\\frac{1}{48}\\left(3x^{4}+4x^{3}-36x^{2}+0+94\\right)$", "<table style='border: 1px solid black;'><tr><td> $x$ </td><td> -3.88 </td><td> -3.00 </td><td> -1.78 </td><td> -1.65 </td><td> 0.00 </td><td> 1.11 </td><td> 2.00 </td></tr>\n<tr><td>$f(x)$ </td><td> 0.00 </td><td> 1.97 </td><td> .27 </td><td> -.00 </td><td> -1.95 </td><td> -1.23 </td><td> -.62 </td></tr>\n<tr><td>$f'(x)$ </td><td> 5.07 </td><td> 0.00 </td><td> -2.05 </td><td> -2.03 </td><td> 0.00 </td><td> 1.01 </td><td> 0.00 </td></tr>\n<tr><td>$f''(x)$ </td><td> -7.88 </td><td> -3.75 </td><td> -.00 </td><td> .27 </td><td> 1.50 </td><td> -.00 </td><td> -2.50 </td></tr></table>\n\n<br><svg height=\"197.02667\" viewBox=\"0 0 302.69333 197.02667\" width=\"302.69333\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"matrix(.13333333 0 0 -.13333333 0 197.02667)\"><path d=\"m65.4844 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m380.418 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m695.348 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1010.28 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1640.14 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m1955.07 74.9336v1259.7264\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m65.4844 74.9336h1889.5856\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m65.4844 389.863h1889.5856\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m65.4844 1019.73h1889.5856\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m65.4844 1334.66h1889.5856\" style=\"fill:none;stroke:#808080;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m65.4844 717.391v-25.192\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m27.1836 619.582h76.6054v49.211h-76.6054z\" fill=\"#fff\"/><path d=\"m27.1836 619.582h76.6054v49.211h-76.6054z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m380.418 717.391v-25.192\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m342.113 619.582h76.606v49.211h-76.606z\" fill=\"#fff\"/><path d=\"m342.113 619.582h76.606v49.211h-76.606z\" style=\"fill:none;stroke:#fff;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m695.348 717.391v-25.192\" style=\"fill:none;stroke:#000;stroke-width:5;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10\"/><path d=\"m657.043 619.582h76.605v49.211h-76.605z\" fill=\"#fff\"/><path d=\"m657.043 619.582h76.605v49.211h-76.605z\" style=\"fill:none; |