extreme f(x)=x^2e^{13x}

Lösung

extrempunkte

f (x) = x^{2} e^{13 x}

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}}), Minimum (0, 0)

Schritte zur Lösung

f^{'} (x) = 2 x e^{13 x} + e^{13 x} \cdot 13 x^{2}

Intervalle finden:

Absteigend

: - \frac{2}{13} < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{2}{13}

x^{2} e^{13 x} : \frac{4}{169 e ^{2}}

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}})

Stecke

x = 0

x^{2} e^{13 x} : 0

Minimum (0, 0)

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}}), Minimum (0, 0)

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e x t re m e f (x) = e^{x^{2} - 4}, (- 2, 2)

e x t re m e f (x, y) = \frac{y}{x} + x^{2} y + 6 x