extreme x^4-8x^3+16x^2+5

Lösung

extrempunkte

x^{4} - 8 x^{3} + 16 x^{2} + 5

Minimum (0, 5), Maximum (2, 21), Minimum (4, 5)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 24 x^{2} + 32 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

x^{4} - 8 x^{3} + 16 x^{2} + 5 : 5

Minimum (0, 5)

Stecke

x = 2

x^{4} - 8 x^{3} + 16 x^{2} + 5 : 21

Maximum (2, 21)

Stecke

x = 4

x^{4} - 8 x^{3} + 16 x^{2} + 5 : 5

Minimum (4, 5)

Minimum (0, 5), Maximum (2, 21), Minimum (4, 5)

a sy m pt o t es f (x) = \frac{x ^{2} - 1}{x + 1}

in v erse y = \frac{4}{3} π x^{3}

in t erce pt s f (x) = - 2 x + 6 y - 12 = 0

d o main f (x) = e^{x} + 2 e^{2 x}

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