extreme f(x)=4x^6-3x^5

Lösung

extrempunkte

f (x) = 4 x^{6} - 3 x^{5}

Sattel (0, 0), Minimum (\frac{5}{8}, - \frac{3125}{65536})

Schritte zur Lösung

f^{'} (x) = 24 x^{5} - 15 x^{4}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{5}{8},

Ansteigend

: \frac{5}{8} < x < \infty

Stecke

x = 0

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

Sattel (0, 0)

Stecke

x = \frac{5}{8}

4 x^{6} - 3 x^{5} : - \frac{3125}{65536}

Minimum (\frac{5}{8}, - \frac{3125}{65536})

Sattel (0, 0), Minimum (\frac{5}{8}, - \frac{3125}{65536})

e x t re m e f (x) = 3 x^{4} + 9 x^{3} + 11

e x t re m e f (x) = 2 x^{2} + 5 x - 1

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

e x t re m e \frac{1}{1 + x ^{2}}

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