extreme f(x)=-3x^4+20x^3-24x^2

Lösung

extrempunkte

f (x) = - 3 x^{4} + 20 x^{3} - 24 x^{2}

Maximum (0, 0), Minimum (1, - 7), Maximum (4, 128)

Schritte zur Lösung

f^{'} (x) = - 12 x^{3} + 60 x^{2} - 48 x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = 0

- 3 x^{4} + 20 x^{3} - 24 x^{2} : 0

Maximum (0, 0)

Stecke

x = 1

- 3 x^{4} + 20 x^{3} - 24 x^{2} : - 7

Minimum (1, - 7)

Stecke

x = 4

- 3 x^{4} + 20 x^{3} - 24 x^{2} : 128

Maximum (4, 128)

Maximum (0, 0), Minimum (1, - 7), Maximum (4, 128)

cr i t i c a l f (x) = x^{2} e^{3 x}

in v erse \frac{8 x}{x + 5}

in v erse f (x) = \frac{1}{6} x^{2} - 1

in v erse \frac{14 x}{x + 14}

r an g e \frac{2 x - 4}{x ^{2} + x - 2}