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Beliebt Funktionen >

extreme e^x(21+9x-x^2)

Lösung

extrempunkte

e^{x} (21 + 9 x - x^{2})

Lösung

Minimum (- 3, - \frac{15}{e ^{3}}), Maximum (10, 11 e^{10})

Schritte zur Lösung

f^{'} (x) = - e^{x} (x + 3) (x - 10)

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 10,

Absteigend

: 10 < x < \infty

Stecke

x = - 3

in

e^{x} (21 + 9 x - x^{2}) : - \frac{15}{e ^{3}}

Minimum (- 3, - \frac{15}{e ^{3}})

Stecke

x = 10

in

e^{x} (21 + 9 x - x^{2}) : 11 e^{10}

Maximum (10, 11 e^{10})

Minimum (- 3, - \frac{15}{e ^{3}}), Maximum (10, 11 e^{10})

Graph

Beliebte Beispiele

extreme f(x)=x^2+y^2+x^2y+7

e x t re m e f (x) = x^{2} + y^{2} + x^{2} y + 7

extreme f(x)=-3/2 x+3

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

extreme f(x,y)=-4x^2-8y^2+4x-16y+1

e x t re m e f (x, y) = - 4 x^{2} - 8 y^{2} + 4 x - 16 y + 1

extreme f(x)=3x^2-3y^2+6=0

e x t re m e f (x) = 3 x^{2} - 3 y^{2} + 6 = 0

extreme f(x)=sqrt(4-x^2),-2<= x<= 2

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