extreme f(x)=x(1-x)^{2/5}

Lösung

extrempunkte

f (x) = x (1 - x)^{\frac{2}{5}}

Maximum (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = \frac{- 7 x + 5}{5 ( 1 - x ) ^{\frac{3}{5}}}

Intervalle finden:

Ansteigend

: - \infty < x < \frac{5}{7},

Absteigend

: \frac{5}{7} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{5}{7}

x (1 - x)^{\frac{2}{5}} : \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}

Maximum (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}})

Stecke

x = 1

x (1 - x)^{\frac{2}{5}} : 0

Minimum (1, 0)

Maximum (\frac{5}{7}, \frac{5 \cdot 2 ^{\frac{2}{5}}}{7 \cdot 7 ^{\frac{2}{5}}}), Minimum (1, 0)

e x t re m e f (x) = x^{2} - 2 x + 2, - 2 \leq x \leq 2

e x t re m e \frac{6}{- 3 x + 2}

e x t re m e ln (x^{2} - 4)

e x t re m e x^{2} y + y^{2} - 4 y

e x t re m e x^{2} + y^{2} + 4 x y