extreme f(x)=x^3-x^2-x-3

Lösung

extrempunkte

f (x) = x^{3} - x^{2} - x - 3

Maximum (- \frac{1}{3}, - \frac{76}{27}), Minimum (1, - 4)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 2 x - 1

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

: 1 < x < \infty

Stecke

x = - \frac{1}{3}

x^{3} - x^{2} - x - 3 : - \frac{76}{27}

Maximum (- \frac{1}{3}, - \frac{76}{27})

Stecke

x = 1

x^{3} - x^{2} - x - 3 : - 4

Minimum (1, - 4)

Maximum (- \frac{1}{3}, - \frac{76}{27}), Minimum (1, - 4)

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

r an g e 4 - z^{2}

r an g e f (x) = (5 x - 2)^{2} (3 x + 4)^{3} (x + 1)^{5}

a sy m pt o t es f (x) = (\frac{2}{3})^{x - 3}

in v erse f (x) = \frac{x + 2}{x + 6}