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

Lösung

extrempunkte

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

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = (x - 3) (3 x - 7)

Intervalle finden:

Ansteigend

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

Absteigend

: \frac{7}{3} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = \frac{7}{3}

(x - 3)^{2} (x - 2) : \frac{4}{27}

Maximum (\frac{7}{3}, \frac{4}{27})

Stecke

x = 3

(x - 3)^{2} (x - 2) : 0

Minimum (3, 0)

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

e x t re m e f (x) = 6 x^{2} - 6 x + 9

e x t re m e f (x) = 2 y^{2} + 2 x y + x^{2} - 16 x - 20 y

e x t re m e - \frac{2}{4 x + x ^{2} - 2}

e x t re m e f (x) = 4 x^{3} + 9 x^{2}

e x t re m e f (x, y) = x^{2} \cdot y^{2} + x^{2} - x \cdot y^{2} - 5 \cdot x - 7