extreme f(x)=(x-1)/(x^2+5x+10)

Lösung

extrempunkte

f (x) = \frac{x - 1}{x ^{2} + 5 x + 10}

Minimum (- 3, - 1), Maximum (5, \frac{1}{15})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 2 x + 15}{( x ^{2} + 5 x + 10 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = - 3

\frac{x - 1}{x ^{2} + 5 x + 10} : - 1

Minimum (- 3, - 1)

Stecke

x = 5

\frac{x - 1}{x ^{2} + 5 x + 10} : \frac{1}{15}

Maximum (5, \frac{1}{15})

Minimum (- 3, - 1), Maximum (5, \frac{1}{15})

d o main f (x) = (\frac{1}{x + 2}) - (\frac{7 x}{x + 2})

sy mm e t ry y = x^{2} + 6 x + 9

in v erse f (x) = x - 13

in f l ec t i o n f (x) = x^{4} - 4 x^{2}

mi d p o in t (- 1, 7), (6, - 2)