extreme e^x(15-x^2)

Lösung

extrempunkte

e^{x} (15 - x^{2})

Minimum (- 5, - \frac{10}{e ^{5}}), Maximum (3, 6 e^{3})

Schritte zur Lösung

f^{'} (x) = - e^{x} (x - 3) (x + 5)

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 5

e^{x} (15 - x^{2}) : - \frac{10}{e ^{5}}

Minimum (- 5, - \frac{10}{e ^{5}})

Stecke

x = 3

e^{x} (15 - x^{2}) : 6 e^{3}

Maximum (3, 6 e^{3})

Minimum (- 5, - \frac{10}{e ^{5}}), Maximum (3, 6 e^{3})

e x t re m e g (x, y) = 16 - x^{2} + y^{2}

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

e x t re m e f (x) = \frac{1 + x ^{2}}{x}

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

e x t re m e f (x) = 100 - x^{2} - y^{2}