extreme (x^4)/4-(x^3)/3-2x^2+4x+3

Lösung

extrempunkte

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

Minimum (- 2, - \frac{19}{3}), Maximum (1, \frac{59}{12}), Minimum (2, \frac{13}{3})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 1,

Absteigend

: 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 2 x^{2} + 4 x + 3 : - \frac{19}{3}

Minimum (- 2, - \frac{19}{3})

Stecke

x = 1

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 2 x^{2} + 4 x + 3 : \frac{59}{12}

Maximum (1, \frac{59}{12})

Stecke

x = 2

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 2 x^{2} + 4 x + 3 : \frac{13}{3}

Minimum (2, \frac{13}{3})

Minimum (- 2, - \frac{19}{3}), Maximum (1, \frac{59}{12}), Minimum (2, \frac{13}{3})

e x t re m e f (x, y) = 4 x y - x^{2} - y^{2} - 14 x + 4 y + 10

e x t re m e y = \frac{sin ( x )}{x} {- 2, π \leq x \leq 2 π}

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

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

e x t re m e f (x) = \frac{1}{3 x ^{3} - 9 x + 2}