extreme x^3-6x^2+2x+4

Lösung

extrempunkte

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

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 40), Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 40 - 830)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{10}{3} + 2,

Absteigend

: - \frac{10}{3} + 2 < x < \frac{10}{3} + 2,

Ansteigend

: \frac{10}{3} + 2 < x < \infty

Stecke

x = \frac{6 - 30}{3}

x^{3} - 6 x^{2} + 2 x + 4 : \frac{288 - 52 30}{9} + 830 - 40

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 40)

Stecke

x = \frac{6 + 30}{3}

x^{3} - 6 x^{2} + 2 x + 4 : \frac{288 + 52 30}{9} - 40 - 830

Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 40 - 830)

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 40), Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 40 - 830)

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

e x t re m e f (x) = - 7 x^{3} + 21 x + 5

e x t re m e f (x) = 0.001 x^{2} + 2.4 x - 90

e x t re m e f (x, y) = 8 x^{3} - 5 x^{2} y + 3 x y^{2}

e x t re m e f (x) = tan (\frac{π x}{20}), 0 \leq x \leq 5