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Version 6.2 von Dirk Tebbe am 2025/10/13 15:11
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2 [[image:Kosinusfunktion.svg||width="450" style="display:block;margin-left:auto;margin-right:auto"]]
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4 2.
5 {{formula}}h(x)=cos(\frac{\pi}{4}x)+1{{/formula}}
6 {{formula}}h'(x)=\frac{\pi}{4}\cdot (-sin(\frac{\pi}{4}x))+1=-\frac{\pi}{4} sin(\frac{\pi}{4}x){{/formula}}
7 {{formula}}h'(6)=-\frac{\pi}{4}sin(\frac{\pi}{4}\cdot 6)=\frac{\pi}{4}{{/formula}}
8 {{formula}}h(6)=1{{/formula}}
9 Einsetzen von {{formula}}m=\frac{\pi}{4}{{/formula}} und {{formula}}P(6|1){{/formula}}in {{formula}}y=mx+c{{/formula}} liefert {{formula}}c=1-\frac{3}{2}\pi{{/formula}}.
10 {{formula}}t: y=\frac{\pi}{4}x+1-\frac{3}{2}\pi{{/formula}}
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12 3.
13 {{formula}}h'(x)=m{{/formula}}
14 {{formula}}-\frac{\pi}{4} sin(\frac{\pi}{4}x)=2{{/formula}}