\( f(x)=10 x^{3}+90 x^{2}-480 x-27 \)
Extremwerte \( f^{\prime}(x)=0 \)
\( f^{\prime}(x)=30 x^{2}+180 x-480 \)
\( 30 x^{2}+180 x-480=0 \mid: 30 \)
\( x^{2}+6 x-16=0 \mid+16 \)
\( x^{2}+6 x=16 \mid+q \cdot E \cdot\left(\frac{6}{2}\right)^{2} \)
\( x^{2}+6 x+9=16+9 \)
\( (x+3)^{2}=25 \)
\( x_{1}=-3+5=2 \rightarrow y_{1}=\ldots \)
\( x_{2}=-3-5=-8 \rightarrow y_{2}=\ldots \)
Art des Extremwertes:
\( f^{\prime \prime}(x)=60 x+180 \)
\( f^{\cdots}(2)=60 \cdot 2+180>0 \rightarrow \) Minimum
\( f^{\prime} \cdot(-8)=60 \cdot(-8)+180<0 \rightarrow \) Maximum
Wendepunkt:
\( f^{\prime \prime}(x)=0 \)
\( 60 x+180=0 \)
\( x=-3 \rightarrow y=\ldots \)
\( \mathrm{mfG} \)
Moliets
