extreme f(x)=(x^8)/(e^{7x)}

Lösung

extrempunkte

f (x) = \frac{x ^{8}}{e ^{7 x}}

Minimum (0, 0), Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{7} ( 8 - 7 x )}{e ^{7 x}}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{8}{7},

Absteigend

: \frac{8}{7} < x < \infty

Stecke

x = 0

\frac{x ^{8}}{e ^{7 x}} : 0

Minimum (0, 0)

Stecke

x = \frac{8}{7}

\frac{x ^{8}}{e ^{7 x}} : \frac{16777216}{5764801 e ^{8}}

Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

Minimum (0, 0), Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

e x t re m e - \frac{5}{1 + x ^{2}}

e x t re m e f (x) = - \frac{1}{6} x^{3} + \frac{3}{2} x^{2} + \frac{5}{2} x - \frac{11}{6}

e x t re m e f (x) = 3 x - t

e x t re m e f (x) = - 4 x^{\frac{5}{3}} + 7 3 x

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