extreme f(x)=27x^3-9x+1

Lösung

extrempunkte

f (x) = 27 x^{3} - 9 x + 1

Maximum (- \frac{1}{3}, 3), Minimum (\frac{1}{3}, - 1)

Schritte zur Lösung

f^{'} (x) = 81 x^{2} - 9

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{3},

Absteigend

: - \frac{1}{3} < x < \frac{1}{3},

Ansteigend

: \frac{1}{3} < x < \infty

Stecke

x = - \frac{1}{3}

27 x^{3} - 9 x + 1 : 3

Maximum (- \frac{1}{3}, 3)

Stecke

x = \frac{1}{3}

27 x^{3} - 9 x + 1 : - 1

Minimum (\frac{1}{3}, - 1)

Maximum (- \frac{1}{3}, 3), Minimum (\frac{1}{3}, - 1)

a sy m pt o t es f (x) = \frac{3 x + 12}{- 12 x + 4}

d o main f (x) = \frac{7 x + 2}{x ^{2} - 5 x + 6}

d o main f (x) = 3 x - 3

a sy m pt o t es 4^{x}

p a r i t y f (x) = - x^{3} + 5 x - 2