extreme f(x)=5x^4+5x^3+7

Lösung

extrempunkte

f (x) = 5 x^{4} + 5 x^{3} + 7

Minimum (- \frac{3}{4}, \frac{1657}{256}), Sattel (0, 7)

Schritte zur Lösung

f^{'} (x) = 20 x^{3} + 15 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{4},

Ansteigend

: - \frac{3}{4} < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{3}{4}

5 x^{4} + 5 x^{3} + 7 : \frac{1657}{256}

Minimum (- \frac{3}{4}, \frac{1657}{256})

Stecke

x = 0

5 x^{4} + 5 x^{3} + 7 : 7

Sattel (0, 7)

Minimum (- \frac{3}{4}, \frac{1657}{256}), Sattel (0, 7)

e x t re m e f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15

e x t re m e f (x, y) = x^{2} + y^{2} - 2 x - 6 y + 14

f (t) = 2 x

e x t re m e T (x, y) = (x + 3 y, - x + 5 y)

e x t re m e f (x) = x (12 - 2 x)^{2}