extreme f(x)=x^9-x^7

Lösung

extrempunkte

f (x) = x^{9} - x^{7}

Maximum (- \frac{7}{3}, \frac{686 7}{19683}), Sattel (0, 0), Minimum (\frac{7}{3}, - \frac{686 7}{19683})

Schritte zur Lösung

f^{'} (x) = 9 x^{8} - 7 x^{6}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7}{3},

Absteigend

: - \frac{7}{3} < x < 0,

Absteigend

: 0 < x < \frac{7}{3},

Ansteigend

: \frac{7}{3} < x < \infty

Stecke

x = - \frac{7}{3}

x^{9} - x^{7} : \frac{686 7}{19683}

Maximum (- \frac{7}{3}, \frac{686 7}{19683})

Stecke

x = 0

x^{9} - x^{7} : 0

Sattel (0, 0)

Stecke

x = \frac{7}{3}

x^{9} - x^{7} : - \frac{686 7}{19683}

Minimum (\frac{7}{3}, - \frac{686 7}{19683})

Maximum (- \frac{7}{3}, \frac{686 7}{19683}), Sattel (0, 0), Minimum (\frac{7}{3}, - \frac{686 7}{19683})

e x t re m e 3 x^{4} + 3 y^{4} - 2 x y

e x t re m e f (x) = 150 x + 18 x^{2} - 1.5 x^{3}

e x t re m e f (x) = sin^{2} (2 x) - cos^{2} (2 x) - 1

e x t re m e f (x) = 2 x - 4 cos (x), - 2 \leq x \leq 0

e x t re m e f (x) = (x + 1) ln^{2} (x + 1)