extreme f(x)=x^3-27x+7

Lösung

extrempunkte

f (x) = x^{3} - 27 x + 7

Maximum (- 3, 61), Minimum (3, - 47)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 27

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

x^{3} - 27 x + 7 : 61

Maximum (- 3, 61)

Stecke

x = 3

x^{3} - 27 x + 7 : - 47

Minimum (3, - 47)

Maximum (- 3, 61), Minimum (3, - 47)

e x t re m e f (x) = \frac{10}{3} x^{3} - 11 x^{2} + 12 x - 24

e x t re m e \frac{x}{x ^{2} + 1}

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

e x t re m e f (x) = 5 x - 60 x^{\frac{1}{3}}

e x t re m e f (x) = \frac{1}{6} (x^{3} - 6 x^{2} + 9 x + 6)