extreme f(x)=x^2e^{1-x}

Lösung

extrempunkte

f (x) = x^{2} e^{1 - x}

Minimum (0, 0), Maximum (2, \frac{4}{e})

Schritte zur Lösung

f^{'} (x) = e^{1 - x} x (2 - x)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

x^{2} e^{1 - x} : 0

Minimum (0, 0)

Stecke

x = 2

x^{2} e^{1 - x} : \frac{4}{e}

Maximum (2, \frac{4}{e})

Minimum (0, 0), Maximum (2, \frac{4}{e})

e x t re m e (3 - x) (x - 5)^{2}

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

e x t re m e f (x) = x^{3} + y^{3} + 9 x^{2} - 9 y^{2} - 2

e x t re m e f (x) = \frac{( x )}{( 6 x + 2 )}, 5 \leq x \leq 8

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