extreme f(x)= 1/3 x^3-2x^2+3x-4

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4

Maximum (1, - \frac{8}{3}), Minimum (3, - 4)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 1,

Absteigend

: 1 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = 1

\frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4 : - \frac{8}{3}

Maximum (1, - \frac{8}{3})

Stecke

x = 3

\frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4 : - 4

Minimum (3, - 4)

Maximum (1, - \frac{8}{3}), Minimum (3, - 4)

e x t re m e f (x) = sin (2 x), 0 \leq x \leq 2 π

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

e x t re m e f (x) = \frac{1}{x} + ln (x), 0.5 \leq x \leq 4

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

e x t re m e f (x, y) = 2 x^{3} - 3 x^{2} y - 12 x^{2} - 3 y^{2}