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Beliebt Funktionen >

extreme f(x)=1+1/x+5/(x^2)+1/(x^3)

Lösung

extrempunkte

f (x) = 1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}}

Lösung

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1), Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Schritte zur Lösung

f^{'} (x) = - \frac{1}{x ^{2}} - \frac{10}{x ^{3}} - \frac{3}{x ^{4}}

Intervalle finden:

Absteigend

: - \infty < x < - 5 - 22,

Ansteigend

: - 5 - 22 < x < - 5 + 22,

Absteigend

: - 5 + 22 < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - 5 - 22

in

1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}} : \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Stecke

x = - 5 + 22

in

1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}} : \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1

Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1), Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Graph

Beliebte Beispiele

extreme f(x)=(x^2-0.8x+0.32)/(1.6-2x)

e x t re m e f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

extreme f(x)=3x^2-9x+9xy^2

e x t re m e f (x) = 3 x^{2} - 9 x + 9 x y^{2}

extreme f(x)=|(x-2)/(x+5)|-3

e x t re m e f (x) = \frac{x - 2}{x + 5} - 3

extreme 2x^4-x^2+5

e x t re m e 2 x^{4} - x^{2} + 5

extreme f(x)=7x^9-9x^7-5(-3.4)

e x t re m e f (x) = 7 x^{9} - 9 x^{7} - 5 (- 3.4)