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Also liegt eine reelle Wurzel zwischen 6.5 und 7, und da es nur eine positive Extremstelle mit fallendem Verlauf nach oben, und \( f(w) \to \infty \) für \( w \to \infty \), und \( f(w) < 0 \) bei kleinen \( w \), gibt es nur **eine** reelle Wurzel (die andere zwei sind komplex oder negativ).
Prüfe Vorzeichenwechsel: \( f(0) = -18 < 0 \), \( f(1) = 1 - 8 + 9 - 18 = -16 < 0 \), \( f(2) = 8 - 32 + 18 - 18 = -24 < 0 \), \( f(3) = 27 - 72 + 27 - 18 = -36 < 0 \), \( f(4) = 64 - 128 + 36 - 18 = -46 < 0 \), \( f(5) = -48 < 0 \), \( f(6) = -36 < 0 \), \( f(6.7) \approx 302.5 - 360.88 + 60.3 - 18 \approx -16.08 \), \( f(6.9) \approx 328.5 - 383.28 + 62.1 - 18 \approx -0.68 \), \( f(6.95) \approx 334.5 - 388.18 + 62.55 - 18 \approx 0.87 > 0 \).
Also eine reelle Wurzel zwischen 6.9 und 6.95, und da es nur eine reelle Wurzel ist (nach Ableitung und Graphie-Analyse), und zwei komplexe, dann gibt es nur **eine** reelle \( w \), also nur **eine** reelle \( v \).

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