extreme f(x)=x^4-200x^2+10000

Lösung

extrempunkte

f (x) = x^{4} - 200 x^{2} + 10000

Minimum (- 10, 0), Maximum (0, 10000), Minimum (10, 0)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 400 x

Intervalle finden:

Absteigend

: - \infty < x < - 10,

Ansteigend

: - 10 < x < 0,

Absteigend

: 0 < x < 10,

Ansteigend

: 10 < x < \infty

Stecke

x = - 10

x^{4} - 200 x^{2} + 10000 : 0

Minimum (- 10, 0)

Stecke

x = 0

x^{4} - 200 x^{2} + 10000 : 10000

Maximum (0, 10000)

Stecke

x = 10

x^{4} - 200 x^{2} + 10000 : 0

Minimum (10, 0)

Minimum (- 10, 0), Maximum (0, 10000), Minimum (10, 0)

in t erce pt s y = x + 6

cr i t i c a l f (x) = 2 x^{3} - 3 x^{2} - 12 x + 1

in v erse f (x) = \frac{( x - 5 )}{3}

d o main y = \frac{1}{x - 8}

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