extreme x^4-5x^2

Lösung

extrempunkte

x^{4} - 5 x^{2}

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 10 x

Intervalle finden:

Absteigend

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

Ansteigend

: - \frac{5}{2} < x < 0,

Absteigend

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

Ansteigend

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

Stecke

x = - \frac{5}{2}

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (- \frac{5}{2}, - \frac{25}{4})

Stecke

x = 0

x^{4} - 5 x^{2} : 0

Maximum (0, 0)

Stecke

x = \frac{5}{2}

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (\frac{5}{2}, - \frac{25}{4})

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

e x t re m e f (x) = y^{3} - x^{3} - 2 x y + 6

e x t re m e f (x) = 7 θ - 9 sin (θ)

e x t re m e f (x, y) = x y^{2} + 3 x y - x + 2

e x t re m e f (x) = (\frac{1}{9} x^{2} + y^{2}) e^{\frac{- x}{3} + y}

e x t re m e f (x) = 16 x^{3} (x + 1)^{2}