extreme e^{2x}(x^2-2)

Lösung

extrempunkte

e^{2 x} (x^{2} - 2)

Maximum (- 2, \frac{2}{e ^{4}}), Minimum (1, - e^{2})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

e^{2 x} (x^{2} - 2) : \frac{2}{e ^{4}}

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

Stecke

x = 1

e^{2 x} (x^{2} - 2) : - e^{2}

Minimum (1, - e^{2})

Maximum (- 2, \frac{2}{e ^{4}}), Minimum (1, - e^{2})

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

e x t re m e f (x) = \frac{( x ^{2} - 7 )}{x + 4}

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

e x t re m e f (x) = \frac{ln ( x )}{x ^{10}}

e x t re m e f (x, y) = \frac{7}{- 91 x ^{2} - 3 y ^{2} + 9}