extreme 2800x-x^3+3x^2+80x-500

Lösung

extrempunkte

2800 x - x^{3} + 3 x^{2} + 80 x - 500

Minimum (- 30, - 57200), Maximum (32, 61964)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 6 x + 2880

Intervalle finden:

Absteigend

: - \infty < x < - 30,

Ansteigend

: - 30 < x < 32,

Absteigend

: 32 < x < \infty

Stecke

x = - 30

2800 x - x^{3} + 3 x^{2} + 80 x - 500 : - 57200

Minimum (- 30, - 57200)

Stecke

x = 32

2800 x - x^{3} + 3 x^{2} + 80 x - 500 : 61964

Maximum (32, 61964)

Minimum (- 30, - 57200), Maximum (32, 61964)

e x t re m e y = 5 - (x + 1)^{2}

e x t re m e f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

e x t re m e f (x) = x - 4 x

e x t re m e f (x) = x^{2} + \frac{360}{x}, [0, \infty]

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