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Zuletzt geändert von Dirk Tebbe am 2025/10/13 12:28
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1 1.
2 {{formula}}f(x)=\frac{1}{5}x^3-\frac{16}{5}x{{/formula}}
3 {{formula}}f'(x)=\frac{3}{5}x^2-\frac{16}{5}{{/formula}}
4 {{formula}}f'(3)=\frac{11}{5}{{/formula}}
5 {{formula}}f(3)=-\frac{21}{5}{{/formula}}
6 Einsetzen von {{formula}}m=\frac{11}{5}{{/formula}} und {{formula}}P(3|-\frac{21}{5}){{/formula}} in {{formula}}y=mx+c{{/formula}}:
7 {{formula}}-\frac{21}{5}=\frac{11}{5}\cdot 3+c{{/formula}}
8 {{formula}}t: y= \frac{11}{5}x-\frac{54}{5}{{/formula}}
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10
11 2.
12 Variante 1: {{formula}}f'(x)=m_t{{/formula}}
13 {{formula}}\frac{3}{5}x^2-\frac{16}{5}=\frac{11}{5}{{/formula}}
14 {{formula}}3x^2=27{{/formula}}
15 {{formula}}x^2=9{{/formula}}
16 {{formula}}x_1=3{{/formula}} und {{formula}}x_2=-3{{/formula}}
17 {{formula}}f(-3)=\frac{21}{5}=g(-3){{/formula}}
18
19 Variante 2: Argumentation mit Punktsymmetrie