extreme f(x)= 1/3 x^3-2x^2-5x-10

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10

Maximum (- 1, - \frac{22}{3}), Minimum (5, - \frac{130}{3})

Schritte zur Lösung

f^{'} (x) = x^{2} - 4 x - 5

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = - 1

\frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10 : - \frac{22}{3}

Maximum (- 1, - \frac{22}{3})

Stecke

x = 5

\frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10 : - \frac{130}{3}

Minimum (5, - \frac{130}{3})

Maximum (- 1, - \frac{22}{3}), Minimum (5, - \frac{130}{3})

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

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

e x t re m e f (x) = 8 (1 + \frac{1}{x} + \frac{1}{x ^{2}})

e x t re m e f (x) = 2 x^{3} + 6 x^{2} - 48 x + 7

e x t re m e x^{4} - 5 x^{2}