extreme f(x)=(x^3)/3-10x^2+75x+20

Lösung

extrempunkte

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

Maximum (5, \frac{560}{3}), Minimum (15, 20)

Schritte zur Lösung

f^{'} (x) = x^{2} - 20 x + 75

Intervalle finden:

Ansteigend

: - \infty < x < 5,

Absteigend

: 5 < x < 15,

Ansteigend

: 15 < x < \infty

Stecke

x = 5

\frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20 : \frac{560}{3}

Maximum (5, \frac{560}{3})

Stecke

x = 15

\frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20 : 20

Minimum (15, 20)

Maximum (5, \frac{560}{3}), Minimum (15, 20)

e x t re m e \frac{x ^{3} + 1}{x + 1}

e x t re m e f (x) = 3 x, - 27 \leq x \leq 8

e x t re m e 6 y = 2 x^{3} - 27 x^{2} + 108 x

e x t re m e ∣ x ∣ + ∣ x + 1 ∣ + x^{2} + 1

e x t re m e y = x z