extreme (x-1)^2(x-2)^3

Lösung

extrempunkte

(x - 1)^{2} (x - 2)^{3}

Maximum (1, 0), Minimum (\frac{7}{5}, - \frac{108}{3125}), Sattel (2, 0)

Schritte zur Lösung

f^{'} (x) = (x - 2)^{2} (x - 1) (5 x - 7)

Intervalle finden:

Ansteigend

: - \infty < x < 1,

Absteigend

: 1 < x < \frac{7}{5},

Ansteigend

: \frac{7}{5} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 1

(x - 1)^{2} (x - 2)^{3} : 0

Maximum (1, 0)

Stecke

x = \frac{7}{5}

(x - 1)^{2} (x - 2)^{3} : - \frac{108}{3125}

Minimum (\frac{7}{5}, - \frac{108}{3125})

Stecke

x = 2

(x - 1)^{2} (x - 2)^{3} : 0

Sattel (2, 0)

Maximum (1, 0), Minimum (\frac{7}{5}, - \frac{108}{3125}), Sattel (2, 0)

p er i o d i c i t y f (x) = sin (- \frac{2 x}{3})

a sy m pt o t es f (x) = \frac{3 e ^{x}}{e ^{x} - 2}

e x t re m e f (x) = x^{3} - 8 x^{2} + 2

a sy m pt o t es f (x) = \frac{3 x}{x ^{2} - 3}

s l o p e f (x) = 7 - 5 x