extreme f(x)=x^4e^{-7x}

Lösung

extrempunkte

f (x) = x^{4} e^{- 7 x}

Minimum (0, 0), Maximum (\frac{4}{7}, \frac{256}{2401 e ^{4}})

Schritte zur Lösung

f^{'} (x) = e^{- 7 x} x^{3} (4 - 7 x)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{4}{7},

Absteigend

: \frac{4}{7} < x < \infty

Stecke

x = 0

x^{4} e^{- 7 x} : 0

Minimum (0, 0)

Stecke

x = \frac{4}{7}

x^{4} e^{- 7 x} : \frac{256}{2401 e ^{4}}

Maximum (\frac{4}{7}, \frac{256}{2401 e ^{4}})

Minimum (0, 0), Maximum (\frac{4}{7}, \frac{256}{2401 e ^{4}})

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

e x t re m e y = 8 + \frac{2}{x}

e x t re m e f (x) = 49 - x^{2}, (- 7, 7)

e x t re m e 40 x^{3} + 9 x^{2} - 12 x - 8

e x t re m e f (x, y) = (x^{2} + 3 y^{2}) e^{1 - x^{2} - y^{2}}