extreme f(x)=(2x^2-5x)/(2x+7)

Lösung

extrempunkte

f (x) = \frac{2 x ^{2} - 5 x}{2 x + 7}

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21}), Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

Schritte zur Lösung

f^{'} (x) = \frac{4 x ^{2} + 28 x - 35}{( 2 x + 7 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7 + 2 21}{2},

Absteigend

: - \frac{7 + 2 21}{2} < x < - \frac{7}{2},

Absteigend

: - \frac{7}{2} < x < \frac{2 21 - 7}{2},

Ansteigend

: \frac{2 21 - 7}{2} < x < \infty

Stecke

x = - \frac{7 + 2 21}{2}

\frac{2 x ^{2} - 5 x}{2 x + 7} : - \frac{84 + 19 21}{2 21}

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21})

Stecke

x = \frac{- 7 + 2 21}{2}

\frac{2 x ^{2} - 5 x}{2 x + 7} : \frac{84 - 19 21}{2 21}

Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21}), Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

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

e x t re m e f (x) = y (3 x - 5)

e x t re m e f (x) = 3 x - 7

e x t re m e f (x) = 2 x - 24 x^{\frac{1}{3}}

e x t re m e f (x) = - \frac{1}{6000} x + \frac{85}{6}