extreme (4x^2-3x^4)/(2x)

Lösung

extrempunkte

\frac{4 x ^{2} - 3 x ^{4}}{2 x}

Minimum (- \frac{2}{3}, - \frac{8}{9}), Maximum (\frac{2}{3}, \frac{8}{9})

Schritte zur Lösung

f^{'} (x) = \frac{1}{2} (- 9 x^{2} + 4)

Intervalle finden:

Absteigend

: - \infty < x < - \frac{2}{3},

Ansteigend

: - \frac{2}{3} < x < 0,

Ansteigend

: 0 < x < \frac{2}{3},

Absteigend

: \frac{2}{3} < x < \infty

Stecke

x = - \frac{2}{3}

\frac{4 x ^{2} - 3 x ^{4}}{2 x} : - \frac{8}{9}

Minimum (- \frac{2}{3}, - \frac{8}{9})

Stecke

x = \frac{2}{3}

\frac{4 x ^{2} - 3 x ^{4}}{2 x} : \frac{8}{9}

Maximum (\frac{2}{3}, \frac{8}{9})

Minimum (- \frac{2}{3}, - \frac{8}{9}), Maximum (\frac{2}{3}, \frac{8}{9})

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

e x t re m e f (x) = - 5 x^{6} ln (x)

e x t re m e f (x, y) = x^{2} - y^{2} + 1

e x t re m e f (x) = \frac{x ^{2} - 16 x + 64}{x - 10}

e x t re m e f (x) = x^{3} + y^{3} - 33 x y