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

Lösung

extrempunkte

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

Maximum (- 1, \frac{3}{2}), Minimum (1, \frac{1}{2})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

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

Maximum (- 1, \frac{3}{2})

Stecke

x = 1

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

Minimum (1, \frac{1}{2})

Maximum (- 1, \frac{3}{2}), Minimum (1, \frac{1}{2})

e x t re m e f (x) = 7 + 3 x + x^{2}

e x t re m e - 0.25 x^{2} + 40 x + 300

e x t re m e x + cos (x)

e x t re m e f (x) = \frac{900 x}{10 + 45 x}

e x t re m e \frac{5 x}{x ^{2} - 1}