extreme 3x^4-24x^3+48x^2

Lösung

extrempunkte

3 x^{4} - 24 x^{3} + 48 x^{2}

Minimum (0, 0), Maximum (2, 48), Minimum (4, 0)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 72 x^{2} + 96 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

3 x^{4} - 24 x^{3} + 48 x^{2} : 0

Minimum (0, 0)

Stecke

x = 2

3 x^{4} - 24 x^{3} + 48 x^{2} : 48

Maximum (2, 48)

Stecke

x = 4

3 x^{4} - 24 x^{3} + 48 x^{2} : 0

Minimum (4, 0)

Minimum (0, 0), Maximum (2, 48), Minimum (4, 0)

in f l ec t i o n (x - 1)^{4} \cdot (x - 3)^{2}

a sy m pt o t es \frac{6 - 3 x}{x - 4}

a sy m pt o t es f (x) = \frac{5}{x ^{2} - 16}

l in e (0, 20), (13500, 4.5)

in v erse y = \frac{( x - 4 )}{( x + 1 )}