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t²

Seite 124 Nummer 2.g.). f t (x) = 1. x 4 -x². t². f t (x) = 1. Gegeben :. x 4 -x². t². Funktion :. Nullstellen : f t (x)=0. 1. 0 =. x 4 -x². / x² - ausklammern. t². 1. 0 = x² * (. x² - 1 ). t². x 1,2 =0. 1. x² - 1 .

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t²

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  1. Seite 124 Nummer 2.g.) ft (x) = 1 x4-x² t² ft (x) = 1 Gegeben: x4-x² t² Funktion: Nullstellen: ft(x)=0 1 0 = x4-x² / x² - ausklammern t² 1 0 = x² * ( x² - 1 ) t² x1,2=0 1 x² - 1 / + 1 0 = t² 1 x² 1 = / * t² t² 1t² = x² / Wurzel x3,4 = + t, - t Nst1 (0/0); Nst2 (0/0); Nst3 ( t /0 ); Nst4 ( -t / 0) 4 Ableitungen: ft‘(x) = x3-2x t² 12 ft‘‘(x) = x2-2 t² 24 x ft‘‘‘(x) = t² Extrema: ft‘(x) = 0 4 / x - ausklammern x3-2x 0 = t² 4 0 = x * ( x² -2) t² 4 0 = x² -2 / *t² / /4 + 1/2 t² x1=0

  2. x2,3 = + - Wurzel aus ½ t² ( + Wurzel aus 1/2 t² / -1/4t²) ft‘‘(Wurzel aus ½ t²) = 4 > 0 = TP TP ( - Wurzel aus ½ t²/-1/4t²) Wegen der Achsensymmetrie gilt: ft‘‘(0) = -2 ft‘‘(0) = 0 HP (0/0) ft‘‘(x) = 0 Wendepunkte: 12 x2-2 0 = t² x1,2 = + - Wurzel aus 1/6 t² ft‘‘‘(+ Wurzel aus 1/6t²) <> 0 ft‘‘‘(+ Wurzel aus 1/6t²) <> 0 WP ( + Wurzel aus 1/6t² / -5/36t²) WP ( - Wurzel aus 1/6t² / -5/36t²) ft‘‘‘(- Wurzel aus 1/6t²) <> 0 Zeichnung: t=3

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