extreme f(x)=x(5-x)(8-x)

Lösung

extrempunkte

f (x) = x (5 - x) (8 - x)

Maximum (2, 36), Minimum (\frac{20}{3}, - \frac{400}{27})

Schritte zur Lösung

f^{'} (x) = (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 (5 - x) (8 - x) : 36

Maximum (2, 36)

Stecke

x = \frac{20}{3}

x (5 - x) (8 - x) : - \frac{400}{27}

Minimum (\frac{20}{3}, - \frac{400}{27})

Maximum (2, 36), Minimum (\frac{20}{3}, - \frac{400}{27})

e x t re m e f (x) = x^{4} - 8 x^{3} + 16 x^{2} + 6

e x t re m e f (x) = 2 x^{2} - 10 x + 5, 0 \leq x \leq 7

e x t re m e sin (4 x)

e x t re m e f (x) = \frac{( x ^{2} - 4 x + 4 )}{x - 8}

e x t re m e f (x) = \frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20