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

Lösung

extrempunkte

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

Maximum (\frac{1 - 7}{3}, \frac{14 7 - 20}{27}), Minimum (\frac{1 + 7}{3}, \frac{- 20 - 14 7}{27})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 7 + 1}{3},

Absteigend

: \frac{- 7 + 1}{3} < x < \frac{7 + 1}{3},

Ansteigend

: \frac{7 + 1}{3} < x < \infty

Stecke

x = \frac{1 - 7}{3}

x^{3} - x^{2} - 2 x : \frac{14 7 - 20}{27}

Maximum (\frac{1 - 7}{3}, \frac{14 7 - 20}{27})

Stecke

x = \frac{1 + 7}{3}

x^{3} - x^{2} - 2 x : \frac{- 20 - 14 7}{27}

Minimum (\frac{1 + 7}{3}, \frac{- 20 - 14 7}{27})

Maximum (\frac{1 - 7}{3}, \frac{14 7 - 20}{27}), Minimum (\frac{1 + 7}{3}, \frac{- 20 - 14 7}{27})

p er p e n d i c u l a r f = \frac{8}{5}

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

d o main f (x) = 15 - (\frac{x}{8.345})

d o main f (x) = x^{2} - 12 x + 36

in v erse f (x) = 9 x + 4