extreme g(x)=(x^3)/((x+1))

Lösung

extrempunkte

g (x) = \frac{x ^{3}}{( x + 1 )}

Minimum (- \frac{3}{2}, \frac{27}{4}), Sattel (0, 0)

Schritte zur Lösung

f^{'} (x) = \frac{2 x ^{3} + 3 x ^{2}}{( x + 1 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

: - \frac{3}{2} < x < - 1,

Ansteigend

: - 1 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{3}{2}

\frac{x ^{3}}{x + 1} : \frac{27}{4}

Minimum (- \frac{3}{2}, \frac{27}{4})

Stecke

x = 0

\frac{x ^{3}}{x + 1} : 0

Sattel (0, 0)

Minimum (- \frac{3}{2}, \frac{27}{4}), Sattel (0, 0)

e x t re m e f (x) = x^{\frac{5}{4}} - 80 x^{\frac{1}{4}}

e x t re m e f (x) = 5 + 6 x - x^{2}, 0 \leq x \leq 4

e x t re m e y = 2 x^{3} - 15 x^{2} + 24 x - 5

e x t re m e f (x) = - 7 x^{2} + 42 x + 5

e x t re m e f (x) = 2 x^{2} + 2 x y + y^{2} + 2 x - 3