extreme f(x)=-2/3 x^3+9x^2-28x+1

Lösung

extrempunkte

f (x) = - \frac{2}{3} x^{3} + 9 x^{2} - 28 x + 1

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

Schritte zur Lösung

f^{'} (x) = - 2 x^{2} + 18 x - 28

Intervalle finden:

Absteigend

: - \infty < x < 2,

Ansteigend

: 2 < x < 7,

Absteigend

: 7 < x < \infty

Stecke

x = 2

- \frac{2}{3} x^{3} + 9 x^{2} - 28 x + 1 : - \frac{73}{3}

Minimum (2, - \frac{73}{3})

Stecke

x = 7

- \frac{2}{3} x^{3} + 9 x^{2} - 28 x + 1 : \frac{52}{3}

Maximum (7, \frac{52}{3})

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

e x t re m e f (x) = ln (x^{2} + 4)

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

e x t re m e x^{3} - 8 y^{3} + 4 x y - 8

e x t re m e f (x, y) = 2 x^{2} - 4 x + y^{2} - 6 y + 1

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