extreme f(x)=x^6(1-x)^{18}

Lösung

extrempunkte

f (x) = x^{6} (1 - x)^{18}

Minimum (0, 0), Maximum (\frac{1}{4}, \frac{387420489}{4 ^{24}}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 6 x^{5} (x - 1)^{17} (4 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{1}{4},

Absteigend

: \frac{1}{4} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = 0

x^{6} (1 - x)^{18} : 0

Minimum (0, 0)

Stecke

x = \frac{1}{4}

x^{6} (1 - x)^{18} : \frac{387420489}{4 ^{24}}

Maximum (\frac{1}{4}, \frac{387420489}{4 ^{24}})

Stecke

x = 1

x^{6} (1 - x)^{18} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{1}{4}, \frac{387420489}{4 ^{24}}), Minimum (1, 0)

e x t re m e f (x) = x^{3} - x^{2} - x + 4, - 1 \leq x \leq 2

e x t re m e f (x, y) = - (x^{2} - y^{2}) e^{- x^{2} - y^{2}}

e x t re m e f (x) = x^{2} lo g_{2} (x)

e x t re m e f (x) = - \frac{2 e ^{- 3 x}}{2 - 3 x}

e x t re m e f (x) = x^{2} - 4 x, - \infty < x \leq 4