extreme f(x)=4+15x+6x^2-x^3

Lösung

extrempunkte

f (x) = 4 + 15 x + 6 x^{2} - x^{3}

Minimum (- 1, - 4), Maximum (5, 104)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 12 x + 15

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = - 1

4 + 15 x + 6 x^{2} - x^{3} : - 4

Minimum (- 1, - 4)

Stecke

x = 5

4 + 15 x + 6 x^{2} - x^{3} : 104

Maximum (5, 104)

Minimum (- 1, - 4), Maximum (5, 104)

e x t re m e g (x, y) = 4 x + 9 y

e x t re m e f (x, y) = 2 x^{2} + 3 x y - 3 y^{2} + 5 x - 5 y + 4

e x t re m e f (x) = 2 x - 6 sin (x)

e x t re m e f (x, y) = 2 x^{3} - 6 x y + y^{2} + 500

e x t re m e f (x) = 4 x e^{- x}, 0 \leq x \leq 2