extreme f(x)=-(2x)/(5x^2+8)

Lösung

extrempunkte

f (x) = - \frac{2 x}{5 x ^{2} + 8}

Maximum (- \frac{2 2}{5}, \frac{1}{2 10}), Minimum (\frac{2 2}{5}, - \frac{1}{2 10})

Schritte zur Lösung

f^{'} (x) = - \frac{2 ( - 5 x ^{2} + 8 )}{( 5 x ^{2} + 8 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{2 2}{5},

Absteigend

: - \frac{2 2}{5} < x < \frac{2 2}{5},

Ansteigend

: \frac{2 2}{5} < x < \infty

Stecke

x = - \frac{2 2}{5}

- \frac{2 x}{5 x ^{2} + 8} : \frac{1}{2 10}

Maximum (- \frac{2 2}{5}, \frac{1}{2 10})

Stecke

x = \frac{2 2}{5}

- \frac{2 x}{5 x ^{2} + 8} : - \frac{1}{2 10}

Minimum (\frac{2 2}{5}, - \frac{1}{2 10})

Maximum (- \frac{2 2}{5}, \frac{1}{2 10}), Minimum (\frac{2 2}{5}, - \frac{1}{2 10})

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e x t re m e e^{3 x} (4 - x)

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e x t re m e \frac{ln ( x )}{x ^{8}}