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

Lösung

extrempunkte

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

Maximum (\frac{1 - 10}{3}, \frac{3 + 10}{2}), Minimum (\frac{1 + 10}{3}, \frac{3 - 10}{2})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{1 - 10}{3},

Absteigend

: \frac{1 - 10}{3} < x < \frac{1 + 10}{3},

Ansteigend

: \frac{1 + 10}{3} < x < \infty

Stecke

x = \frac{1 - 10}{3}

\frac{x ^{2} - 3 x + 2}{x ^{2} + 1} : \frac{3 + 10}{2}

Maximum (\frac{1 - 10}{3}, \frac{3 + 10}{2})

Stecke

x = \frac{1 + 10}{3}

\frac{x ^{2} - 3 x + 2}{x ^{2} + 1} : \frac{3 - 10}{2}

Minimum (\frac{1 + 10}{3}, \frac{3 - 10}{2})

Maximum (\frac{1 - 10}{3}, \frac{3 + 10}{2}), Minimum (\frac{1 + 10}{3}, \frac{3 - 10}{2})

cr i t i c a l \frac{e ^{x}}{6 + e ^{x}}

r an g e f (x) = 3 x^{5} - 8 x^{3} + 4 x^{2} - 5 x + 2

r an g e x (13 - 2 x) (11 - 2 x)

d o main f (x) = - 4 x^{2}

d o main \frac{1}{\frac{4}{x - 1} - 2}