extreme f(x)=3x(x-5)^2

Lösung

extrempunkte

f (x) = 3 x (x - 5)^{2}

Maximum (\frac{5}{3}, \frac{500}{9}), Minimum (5, 0)

Schritte zur Lösung

f^{'} (x) = 3 (3 x^{2} - 20 x + 25)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{5}{3},

Absteigend

: \frac{5}{3} < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = \frac{5}{3}

3 x (x - 5)^{2} : \frac{500}{9}

Maximum (\frac{5}{3}, \frac{500}{9})

Stecke

x = 5

3 x (x - 5)^{2} : 0

Minimum (5, 0)

Maximum (\frac{5}{3}, \frac{500}{9}), Minimum (5, 0)

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

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

e x t re m e x^{2} + 4 x y + y^{2} - 40 x - 56 y + 1

e x t re m e f (x, y) = \frac{x ^{3} + 5 x y ^{2}}{y}

e x t re m e f (x) = 6 x^{5} - 15 x^{4} + 10 x^{3}