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Beliebt Funktionen >

extreme f(x)=e^x(24-x^2)

Lösung

extrempunkte

f (x) = e^{x} (24 - x^{2})

Lösung

Minimum (- 6, - \frac{12}{e ^{6}}), Maximum (4, 8 e^{4})

Schritte zur Lösung

f^{'} (x) = - e^{x} (x - 4) (x + 6)

Intervalle finden:

Absteigend

: - \infty < x < - 6,

Ansteigend

: - 6 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 6

in

e^{x} (24 - x^{2}) : - \frac{12}{e ^{6}}

Minimum (- 6, - \frac{12}{e ^{6}})

Stecke

x = 4

in

e^{x} (24 - x^{2}) : 8 e^{4}

Maximum (4, 8 e^{4})

Minimum (- 6, - \frac{12}{e ^{6}}), Maximum (4, 8 e^{4})

Graph

Beliebte Beispiele

extreme f(x,y)=ln(x+y)+x^2-y

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

e x t re m e x^{2} - 2 x

extreme g(x,y)=2x^2+3y^2-7

e x t re m e g (x, y) = 2 x^{2} + 3 y^{2} - 7

extreme f(x,y)=x^3+2xy+y^2-5x

e x t re m e f (x, y) = x^{3} + 2 x y + y^{2} - 5 x

extreme f(x)=x^4-2x^2-3

e x t re m e f (x) = x^{4} - 2 x^{2} - 3