extreme f(x)=x^3-8x^2+3

Lösung

extrempunkte

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

Maximum (0, 3), Minimum (\frac{16}{3}, - \frac{1967}{27})

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 16 x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{16}{3},

Ansteigend

: \frac{16}{3} < x < \infty

Stecke

x = 0

x^{3} - 8 x^{2} + 3 : 3

Maximum (0, 3)

Stecke

x = \frac{16}{3}

x^{3} - 8 x^{2} + 3 : - \frac{1967}{27}

Minimum (\frac{16}{3}, - \frac{1967}{27})

Maximum (0, 3), Minimum (\frac{16}{3}, - \frac{1967}{27})

e x t re m e f (x) = x^{3} - 12 x + 18

e x t re m e f (x) = 2 x^{3} - 20 x + 50 x - 6

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

e x t re m e f (x, y) = 6 x^{2} y - 9 x y

e x t re m e y = \frac{2 ( x + 3 )}{x ^{2} + x - 2}