extreme f(x)=x(7-x)(30-2x)

Lösung

extrempunkte

f (x) = x (7 - x) (30 - 2 x)

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

Schritte zur Lösung

f^{'} (x) = 2 (x - 3) (3 x - 35)

Intervalle finden:

Ansteigend

: - \infty < x < 3,

Absteigend

: 3 < x < \frac{35}{3},

Ansteigend

: \frac{35}{3} < x < \infty

Stecke

x = 3

x (7 - x) (30 - 2 x) : 288

Maximum (3, 288)

Stecke

x = \frac{35}{3}

x (7 - x) (30 - 2 x) : - \frac{9800}{27}

Minimum (\frac{35}{3}, - \frac{9800}{27})

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

e x t re m e S (a, b) = 2 π (a + b)

e x t re m e f (x, y) = - 7 x^{2} + 5 y^{2} - 4 x - 5 y + 5

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

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

e x t re m e P (x, y) = 40 x + 50 y