extreme f(x)=-1000x^3-1000x^2+8000x+1000

Lösung

extrempunkte

f (x) = - 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

Minimum (- 2, - 11000), Maximum (\frac{4}{3}, \frac{203000}{27})

Schritte zur Lösung

f^{'} (x) = - 3000 x^{2} - 2000 x + 8000

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < \frac{4}{3},

Absteigend

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

Stecke

x = - 2

- 1000 x^{3} - 1000 x^{2} + 8000 x + 1000 : - 11000

Minimum (- 2, - 11000)

Stecke

x = \frac{4}{3}

- 1000 x^{3} - 1000 x^{2} + 8000 x + 1000 : \frac{203000}{27}

Maximum (\frac{4}{3}, \frac{203000}{27})

Minimum (- 2, - 11000), Maximum (\frac{4}{3}, \frac{203000}{27})

e x t re m e \frac{1}{x} + ln (x)

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

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

e x t re m e f (x, y) = x^{3} + y^{3} - 15 x y

e x t re m e f (x, y) = 49 - x^{2} - y^{2}