extreme f(x)=x(10-2x)(8-x)

Lösung

extrempunkte

f (x) = x (10 - 2 x) (8 - x)

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

Schritte zur Lösung

f^{'} (x) = 2 (x - 2) (3 x - 20)

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

: 2 < x < \frac{20}{3},

Ansteigend

: \frac{20}{3} < x < \infty

Stecke

x = 2

x (10 - 2 x) (8 - x) : 72

Maximum (2, 72)

Stecke

x = \frac{20}{3}

x (10 - 2 x) (8 - x) : - \frac{800}{27}

Minimum (\frac{20}{3}, - \frac{800}{27})

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

e x t re m e h

e x t re m e f (x) = x^{3} + y^{3} + 2 x^{2} + 4 y^{2} + 6

e x t re m e y = x^{2} + x + 1

e x t re m e f (x) = 1 + 80 x^{3} + 5 x^{4} - 2 x^{5}

e x t re m e f (x) = 18 x y - x^{3} - 9 y^{2}