extreme f(x)=-4x^3+12x^2+36+3

Lösung

extrempunkte

f (x) = - 4 x^{3} + 12 x^{2} + 36 + 3

Minimum (0, 39), Maximum (2, 55)

Schritte zur Lösung

f^{'} (x) = - 12 x^{2} + 24 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

- 4 x^{3} + 12 x^{2} + 36 + 3 : 39

Minimum (0, 39)

Stecke

x = 2

- 4 x^{3} + 12 x^{2} + 36 + 3 : 55

Maximum (2, 55)

Minimum (0, 39), Maximum (2, 55)

e x t re m e f (x) = 3^{\frac{2}{3}} - 2 x (- 1.1)

e x t re m e f (x) = - 0.001 x^{2} + 6 x - 1900

e x t re m e h (x) = 5 (x - 1)^{\frac{2}{3}}, 0 \leq x \leq 2

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

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