extreme f(x)=3x+1+1/(x-1)

Lösung

extrempunkte

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

Maximum (- \frac{1}{3} + 1, 4 - 23), Minimum (\frac{1}{3} + 1, 23 + 4)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{3 - 1}{3},

Absteigend

: \frac{3 - 1}{3} < x < 1,

Absteigend

: 1 < x < \frac{1 + 3}{3},

Ansteigend

: \frac{1 + 3}{3} < x < \infty

Stecke

x = - \frac{1}{3} + 1

3 x + 1 + \frac{1}{x - 1} : 4 - 23

Maximum (- \frac{1}{3} + 1, 4 - 23)

Stecke

x = \frac{1}{3} + 1

3 x + 1 + \frac{1}{x - 1} : 23 + 4

Minimum (\frac{1}{3} + 1, 23 + 4)

Maximum (- \frac{1}{3} + 1, 4 - 23), Minimum (\frac{1}{3} + 1, 23 + 4)

e x t re m e f (x) = 9 x^{5} - 2 x^{4} - 2 x^{3} + 4

e x t re m e 3 x^{2} - 12 x - 15

e x t re m e f (x) = x y + \frac{9}{x} + \frac{3}{y}

e x t re m e f (x) = 27 x - x^{3}

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