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

Lösung

extrempunkte

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

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4), Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 8 x + 3

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 7 + 4}{3},

Absteigend

: \frac{- 7 + 4}{3} < x < \frac{7 + 4}{3},

Ansteigend

: \frac{7 + 4}{3} < x < \infty

Stecke

x = \frac{4 - 7}{3}

x^{3} - 4 x^{2} + 3 x : - 7 + \frac{41 7 - 128}{27} + 4

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4)

Stecke

x = \frac{4 + 7}{3}

x^{3} - 4 x^{2} + 3 x : 7 + \frac{- 128 - 41 7}{27} + 4

Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

Maximum (\frac{4 - 7}{3}, - 7 + \frac{41 7 - 128}{27} + 4), Minimum (\frac{4 + 7}{3}, 7 + \frac{- 128 - 41 7}{27} + 4)

e x t re m e f (x, y) = \frac{1}{3} x^{3} + \frac{1}{3} y^{3} - x y + 4

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 16 y + 85

e x t re m e f (t) = (t - 2) u (t + 5)

e x t re m e f (x, y) = - 4 x^{2} + 7 x y - 3 y^{2} + x + y

e x t re m e - 0.05 x^{2} + 71 x + 200