de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Funktionen >

extreme f(x)=-8x^{5/3}+\sqrt[3]{x}

Lösung

extrempunkte

f (x) = - 8 x^{\frac{5}{3}} + 3 x

Lösung

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Schritte zur Lösung

f^{'} (x) = - \frac{40 x ^{\frac{2}{3}}}{3} + \frac{1}{3 x ^{\frac{2}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{4 0 ^{\frac{3}{4}}},

Ansteigend

: - \frac{1}{4 0 ^{\frac{3}{4}}} < x < 0,

Ansteigend

: 0 < x < \frac{1}{4 0 ^{\frac{3}{4}}},

Absteigend

: \frac{1}{4 0 ^{\frac{3}{4}}} < x < \infty

Stecke

x = - \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

in

- 8 x^{\frac{5}{3}} + 3 x : - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}})

Stecke

x = \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

in

- 8 x^{\frac{5}{3}} + 3 x : - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Graph

Beliebte Beispiele

extreme f(x,y)=xye^{-8y}

e x t re m e f (x, y) = x y e^{- 8 y}

extreme x^3+y^3-6y^2-3x+9

e x t re m e x^{3} + y^{3} - 6 y^{2} - 3 x + 9

extreme f(x)=\sqrt[3]{x}(8-x),0<= x<= 8

e x t re m e f (x) = 3 x (8 - x), 0 \leq x \leq 8

extreme f(x)=\sqrt[3]{x}(8-x)

e x t re m e f (x) = 3 x (8 - x)

extreme y= 1/(x-2)-3

e x t re m e y = \frac{1}{x - 2} - 3