extreme f(x)=(x-1)^2(x+3)

Lösung

extrempunkte

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

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = (x - 1) (3 x + 5)

Intervalle finden:

Ansteigend

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

Absteigend

: - \frac{5}{3} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - \frac{5}{3}

(x - 1)^{2} (x + 3) : \frac{256}{27}

Maximum (- \frac{5}{3}, \frac{256}{27})

Stecke

x = 1

(x - 1)^{2} (x + 3) : 0

Minimum (1, 0)

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

e x t re m e f (x, y) = 4 x^{2} + y^{2}

e x t re m e f (x, y) = x y (1 - x - y)

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

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

e x t re m e f (x) = \frac{x}{( x + 1 ) ^{2}}