extreme f(x)=4x^3-46x^2+120x

Lösung

extrempunkte

f (x) = 4 x^{3} - 46 x^{2} + 120 x

Maximum (\frac{5}{3}, \frac{2450}{27}), Minimum (6, - 72)

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 92 x + 120

Intervalle finden:

Ansteigend

: - \infty < x < \frac{5}{3},

Absteigend

: \frac{5}{3} < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = \frac{5}{3}

4 x^{3} - 46 x^{2} + 120 x : \frac{2450}{27}

Maximum (\frac{5}{3}, \frac{2450}{27})

Stecke

x = 6

4 x^{3} - 46 x^{2} + 120 x : - 72

Minimum (6, - 72)

Maximum (\frac{5}{3}, \frac{2450}{27}), Minimum (6, - 72)

e x t re m e 4 x^{3} - 12 x^{2} + 8 x

e x t re m e f (x) = 4 x^{2} - 6 x y + 5 y^{2} - 20 x + 26 y

e x t re m e y = x^{2} - 12

e x t re m e f (x) = x^{3} e^{(4 - 2 x^{2})}

e x t re m e 22 x^{2}