extreme f(x)=x^2e^{-7x}

Lösung

extrempunkte

f (x) = x^{2} e^{- 7 x}

Minimum (0, 0), Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

Schritte zur Lösung

f^{'} (x) = e^{- 7 x} x (2 - 7 x)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{2}{7},

Absteigend

: \frac{2}{7} < x < \infty

Stecke

x = 0

x^{2} e^{- 7 x} : 0

Minimum (0, 0)

Stecke

x = \frac{2}{7}

x^{2} e^{- 7 x} : \frac{4}{49 e ^{2}}

Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

Minimum (0, 0), Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

in v erse e^{2 l n (3 x)}

a sy m pt o t es f (x) = \frac{x ^{2} + 2}{7 x - 4 x ^{2}}

a sy m pt o t es f (x) = \frac{4}{x ^{2} + 2 x - 8}

r an g e y = - x + 1 - 3

cr i t i c a l f (x) = x^{(\frac{7}{2})} - 7 x^{2}