extreme f(x)= x/(x^2+81)

Lösung

extrempunkte

f (x) = \frac{x}{x ^{2} + 81}

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 9,

Ansteigend

: - 9 < x < 9,

Absteigend

: 9 < x < \infty

Stecke

x = - 9

\frac{x}{x ^{2} + 81} : - \frac{1}{18}

Minimum (- 9, - \frac{1}{18})

Stecke

x = 9

\frac{x}{x ^{2} + 81} : \frac{1}{18}

Maximum (9, \frac{1}{18})

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

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