extreme f(x)=3x^6-7x^5

Lösung

extrempunkte

f (x) = 3 x^{6} - 7 x^{5}

Sattel (0, 0), Minimum (\frac{35}{18}, \frac{3 5 ^{6}}{11337408} - \frac{367653125}{1889568})

Schritte zur Lösung

f^{'} (x) = 18 x^{5} - 35 x^{4}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{35}{18},

Ansteigend

: \frac{35}{18} < x < \infty

Stecke

x = 0

3 x^{6} - 7 x^{5} : 0

Sattel (0, 0)

Stecke

x = \frac{35}{18}

3 x^{6} - 7 x^{5} : \frac{3 5 ^{6}}{11337408} - \frac{367653125}{1889568}

Minimum (\frac{35}{18}, \frac{3 5 ^{6}}{11337408} - \frac{367653125}{1889568})

Sattel (0, 0), Minimum (\frac{35}{18}, \frac{3 5 ^{6}}{11337408} - \frac{367653125}{1889568})

e x t re m e f (x, y) = e^{x^{2} + 3 y^{2} + 15}

e x t re m e g (x) = x^{3} - 2 x^{2} - 4 x + 8

e x t re m e f (x) = x^{3} + 6 x^{2} - 63 x + 5, - 8 \leq x \leq 0

e x t re m e f (x) = 3 x^{2} - 6 x + 24

e x t re m e f (x) = (9 x^{2} + 4 x + 5) (9 y^{2} + 6 y + 6)