extreme f(x)=16x+9/x

Lösung

extrempunkte

f (x) = 16 x + \frac{9}{x}

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

Schritte zur Lösung

f^{'} (x) = 16 - \frac{9}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{4},

Absteigend

: - \frac{3}{4} < x < 0,

Absteigend

: 0 < x < \frac{3}{4},

Ansteigend

: \frac{3}{4} < x < \infty

Stecke

x = - \frac{3}{4}

16 x + \frac{9}{x} : - 24

Maximum (- \frac{3}{4}, - 24)

Stecke

x = \frac{3}{4}

16 x + \frac{9}{x} : 24

Minimum (\frac{3}{4}, 24)

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

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e x t re m e (x + 6)^{\frac{2}{3}}

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