extreme f(x)=1+1/x+9/(x^2)+1/(x^3)

Lösung

extrempunkte

f (x) = 1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}}

Minimum (- 9 - 78, - \frac{52 78 - 459}{9} + 1), Maximum (- 9 + 78, \frac{468 78 + 4131}{535814 1 ^{2} - 60669 0 ^{2} \cdot 78} + 1)

Schritte zur Lösung

f^{'} (x) = - \frac{1}{x ^{2}} - \frac{18}{x ^{3}} - \frac{3}{x ^{4}}

Intervalle finden:

Absteigend

: - \infty < x < - 9 - 78,

Ansteigend

: - 9 - 78 < x < - 9 + 78,

Absteigend

: - 9 + 78 < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - 9 - 78

1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}} : - \frac{52 78 - 459}{9} + 1

Minimum (- 9 - 78, - \frac{52 78 - 459}{9} + 1)

Stecke

x = - 9 + 78

1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}} : \frac{468 78 + 4131}{535814 1 ^{2} - 60669 0 ^{2} \cdot 78} + 1

Maximum (- 9 + 78, \frac{468 78 + 4131}{535814 1 ^{2} - 60669 0 ^{2} \cdot 78} + 1)

Minimum (- 9 - 78, - \frac{52 78 - 459}{9} + 1), Maximum (- 9 + 78, \frac{468 78 + 4131}{535814 1 ^{2} - 60669 0 ^{2} \cdot 78} + 1)

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

e x t re m e 0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000

e x t re m e f (x, y) = x^{2} + 6 x + y^{3} - 6 y^{2}

e x t re m e f (x) = - x^{4} - 17 x^{3} - 106 x^{2} - 290 x - 293

e x t re m e f (x) = sin (4 x), - \frac{π}{6} \leq x \leq \frac{π}{4}