extreme f(x)=(x^5)/5-(4x^4)/4+2

Lösung

extrempunkte

f (x) = \frac{x ^{5}}{5} - \frac{4 x ^{4}}{4} + 2

Maximum (0, 2), Minimum (4, - \frac{246}{5})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

\frac{x ^{5}}{5} - \frac{4 x ^{4}}{4} + 2 : 2

Maximum (0, 2)

Stecke

x = 4

\frac{x ^{5}}{5} - \frac{4 x ^{4}}{4} + 2 : - \frac{246}{5}

Minimum (4, - \frac{246}{5})

Maximum (0, 2), Minimum (4, - \frac{246}{5})

e x t re m e f (x) = \frac{x ^{5}}{5} - \frac{4 x ^{4}}{4} + 6

e x t re m e 3 - x

e x t re m e f (x) = 2 x^{3} - 18 x^{2} + 48 x - 7

e x t re m e x^{3} + y^{3} - 27 x - 48 y - 24

e x t re m e y = \frac{cos ( x )}{1 + sin ^{2} ( x )}