extreme f(x)=x[36-2(x)]^2

Lösung

extrempunkte

f (x) = x [36 - 2 (x)]^{2}

Maximum (6, 3456), Minimum (18, 0)

Schritte zur Lösung

f^{'} (x) = 12 (x - 6) (x - 18)

Intervalle finden:

Ansteigend

: - \infty < x < 6,

Absteigend

: 6 < x < 18,

Ansteigend

: 18 < x < \infty

Stecke

x = 6

x [36 - 2 x]^{2} : 3456

Maximum (6, 3456)

Stecke

x = 18

x [36 - 2 x]^{2} : 0

Minimum (18, 0)

Maximum (6, 3456), Minimum (18, 0)

e x t re m e f (x) = x + 12 - 8

e x t re m e f (x, y) = 4 x y + 120 y - 20 y^{2} - \frac{1}{10} x^{2} y - 90

e x t re m e f (x, y) = 2 x^{2} + 4 y^{2} - 2 x y - 10 x - 2 y + 2

e x t re m e f (x) = \frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

e x t re m e 2 x^{3} + 4 x^{2} - 1