extreme f(x)=6x^5-2x^4

Lösung

extrempunkte

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

Maximum (0, 0), Minimum (\frac{4}{15}, - \frac{512}{253125})

Schritte zur Lösung

f^{'} (x) = 30 x^{4} - 8 x^{3}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{4}{15},

Ansteigend

: \frac{4}{15} < x < \infty

Stecke

x = 0

6 x^{5} - 2 x^{4} : 0

Maximum (0, 0)

Stecke

x = \frac{4}{15}

6 x^{5} - 2 x^{4} : - \frac{512}{253125}

Minimum (\frac{4}{15}, - \frac{512}{253125})

Maximum (0, 0), Minimum (\frac{4}{15}, - \frac{512}{253125})

e x t re m e f (x) = - x^{3} + 3 x^{2} + 2880 x - 500

e x t re m e x^{3} - 3 x^{2} - 9 x + 10

e x t re m e f (x) = x^{5} - \frac{5}{3} x^{3} + 2

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

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