extreme f(x)=x^3-9x^2-21x+9

Lösung

extrempunkte

f (x) = x^{3} - 9 x^{2} - 21 x + 9

Maximum (- 1, 20), Minimum (7, - 236)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 18 x - 21

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 7,

Ansteigend

: 7 < x < \infty

Stecke

x = - 1

x^{3} - 9 x^{2} - 21 x + 9 : 20

Maximum (- 1, 20)

Stecke

x = 7

x^{3} - 9 x^{2} - 21 x + 9 : - 236

Minimum (7, - 236)

Maximum (- 1, 20), Minimum (7, - 236)

e x t re m e f (x) = 4 x^{2} - x - 5

e x t re m e f (x, y) = x^{2} + 14 x y + y^{2}

e x t re m e f (x) = \frac{27 x ^{2}}{( 1 - x ) ^{3}}

e x t re m e f (x) = 345 x^{2} - 3450 x^{3}, 0 \leq x \leq 0.1

e x t re m e f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 2021