extreme f(x)=-3x^4+24x^3-30x^2

Lösung

extrempunkte

f (x) = - 3 x^{4} + 24 x^{3} - 30 x^{2}

Maximum (0, 0), Minimum (1, - 9), Maximum (5, 375)

Schritte zur Lösung

f^{'} (x) = - 12 x^{3} + 72 x^{2} - 60 x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = 0

- 3 x^{4} + 24 x^{3} - 30 x^{2} : 0

Maximum (0, 0)

Stecke

x = 1

- 3 x^{4} + 24 x^{3} - 30 x^{2} : - 9

Minimum (1, - 9)

Stecke

x = 5

- 3 x^{4} + 24 x^{3} - 30 x^{2} : 375

Maximum (5, 375)

Maximum (0, 0), Minimum (1, - 9), Maximum (5, 375)

in v erse f (x) = 3 lo g_{2} (2 x - 8)

p er i o d i c i t y f (x) = - tan (\frac{1}{4} x)

d o main y = cos (3 x)

d o main f (x) = (x - 4)^{2} - 1

in v erse f (x) = - 35 x + 5