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

Lösung

extrempunkte

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

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2), Sattel (0, 2), Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Schritte zur Lösung

f^{'} (x) = 5 x^{4} - 6 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{6}{5},

Absteigend

: - \frac{6}{5} < x < 0,

Absteigend

: 0 < x < \frac{6}{5},

Ansteigend

: \frac{6}{5} < x < \infty

Stecke

x = - \frac{6}{5}

x^{5} - 2 x^{3} + 2 : - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Stecke

x = 0

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

Sattel (0, 2)

Stecke

x = \frac{6}{5}

x^{5} - 2 x^{3} + 2 : (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2

Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2), Sattel (0, 2), Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

e x t re m e f (x) = x (15 - 40 + 2 x) (\frac{40}{2} - x)

e x t re m e f (x) = (3 x^{2} + 3)^{2}

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

e x t re m e f (x) = - 5 sec (x)

e x t re m e f (x) = (1)^{3 n}