extreme y=4x^3-x

Lösung

extrempunkte

y = 4 x^{3} - x

Maximum (- \frac{1}{2 3}, \frac{1}{3 3}), Minimum (\frac{1}{2 3}, - \frac{1}{3 3})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 1

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{2 3},

Absteigend

: - \frac{1}{2 3} < x < \frac{1}{2 3},

Ansteigend

: \frac{1}{2 3} < x < \infty

Stecke

x = - \frac{1}{2 3}

4 x^{3} - x : \frac{1}{3 3}

Maximum (- \frac{1}{2 3}, \frac{1}{3 3})

Stecke

x = \frac{1}{2 3}

4 x^{3} - x : - \frac{1}{3 3}

Minimum (\frac{1}{2 3}, - \frac{1}{3 3})

Maximum (- \frac{1}{2 3}, \frac{1}{3 3}), Minimum (\frac{1}{2 3}, - \frac{1}{3 3})

e x t re m e (\frac{x}{4})^{4} - \frac{4}{3} x^{3} + \frac{1}{2} x^{2} + 6 x + 2

e x t re m e \frac{1}{3} x^{3} - 4 x^{2} + 12 x + 200

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

e x t re m e f (x) = g (t) = 6 t^{4} - 8 t^{3} + 5

e x t re m e f (x) = - \frac{x ^{2}}{8} + \frac{y ^{2}}{78.13} + 8