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

Lösung

extrempunkte

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

Maximum (- 1, \frac{8}{3}), Sattel (0, 2), Minimum (1, \frac{4}{3})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

x^{5} - \frac{5}{3} x^{3} + 2 : \frac{8}{3}

Maximum (- 1, \frac{8}{3})

Stecke

x = 0

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

Sattel (0, 2)

Stecke

x = 1

x^{5} - \frac{5}{3} x^{3} + 2 : \frac{4}{3}

Minimum (1, \frac{4}{3})

Maximum (- 1, \frac{8}{3}), Sattel (0, 2), Minimum (1, \frac{4}{3})

e x t re m e f (x) = x - sin (- x)

e x t re m e y = x x - 6

e x t re m e f (x) = x + 3 - x

e x t re m e f (x) = x (25 - 46 + 2 x) (\frac{46}{2} - x)

e x t re m e f (x) = \frac{2 x ^{3}}{3} - x^{2} + \frac{x}{2} + \frac{1}{2}