extreme y=(x-4)^4(x+3)^3

Lösung

extrempunkte

y = (x - 4)^{4} (x + 3)^{3}

Sattel (- 3, 0), Maximum (0, 6912), Minimum (4, 0)

Schritte zur Lösung

f^{'} (x) = 7 x (x - 4)^{3} (x + 3)^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 3

(x - 4)^{4} (x + 3)^{3} : 0

Sattel (- 3, 0)

Stecke

x = 0

(x - 4)^{4} (x + 3)^{3} : 6912

Maximum (0, 6912)

Stecke

x = 4

(x - 4)^{4} (x + 3)^{3} : 0

Minimum (4, 0)

Sattel (- 3, 0), Maximum (0, 6912), Minimum (4, 0)

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

e x t re m e f (x) = 6 x^{3} - 21 x^{2} + 36 x - 5

e x t re m e f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10

e x t re m e f (x) = 3 - x^{\frac{4}{5}}

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