extreme f(x)=-x^3-x^2+5x+1

Lösung

extrempunkte

f (x) = - x^{3} - x^{2} + 5 x + 1

Minimum (- \frac{5}{3}, - \frac{148}{27}), Maximum (1, 4)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} - 2 x + 5

Intervalle finden:

Absteigend

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

Ansteigend

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

Absteigend

: 1 < x < \infty

Stecke

x = - \frac{5}{3}

- x^{3} - x^{2} + 5 x + 1 : - \frac{148}{27}

Minimum (- \frac{5}{3}, - \frac{148}{27})

Stecke

x = 1

- x^{3} - x^{2} + 5 x + 1 : 4

Maximum (1, 4)

Minimum (- \frac{5}{3}, - \frac{148}{27}), Maximum (1, 4)

e x t re m e \frac{30}{x} + 3 π x^{2}

e x t re m e y = - x^{3} + 6 x^{2}

e x t re m e f (x, y) = - 3 x^{2} + 2 x y - y^{2} + 14 x + 2 y + 10

e x t re m e f (x) = x^{2} lo g_{6} (x)

e x t re m e 250 + 8 x^{3} + x^{4}