extreme f(x)=x^4-x^2

Lösung

extrempunkte

f (x) = x^{4} - x^{2}

Minimum (- \frac{1}{2}, - \frac{1}{4}), Maximum (0, 0), Minimum (\frac{1}{2}, - \frac{1}{4})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 2 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{2},

Ansteigend

: - \frac{1}{2} < x < 0,

Absteigend

: 0 < x < \frac{1}{2},

Ansteigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{1}{2}

x^{4} - x^{2} : - \frac{1}{4}

Minimum (- \frac{1}{2}, - \frac{1}{4})

Stecke

x = 0

x^{4} - x^{2} : 0

Maximum (0, 0)

Stecke

x = \frac{1}{2}

x^{4} - x^{2} : - \frac{1}{4}

Minimum (\frac{1}{2}, - \frac{1}{4})

Minimum (- \frac{1}{2}, - \frac{1}{4}), Maximum (0, 0), Minimum (\frac{1}{2}, - \frac{1}{4})

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

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

e x t re m e f (x) = 100 - x^{2} - y^{2}

e x t re m e f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

e x t re m e f (x) = cos^{2} (x) - 2 sin (x)