extreme 2x^4-x^2+5

Lösung

extrempunkte

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

Minimum (- \frac{1}{2}, \frac{39}{8}), Maximum (0, 5), Minimum (\frac{1}{2}, \frac{39}{8})

Schritte zur Lösung

f^{'} (x) = 8 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}

2 x^{4} - x^{2} + 5 : \frac{39}{8}

Minimum (- \frac{1}{2}, \frac{39}{8})

Stecke

x = 0

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

Maximum (0, 5)

Stecke

x = \frac{1}{2}

2 x^{4} - x^{2} + 5 : \frac{39}{8}

Minimum (\frac{1}{2}, \frac{39}{8})

Minimum (- \frac{1}{2}, \frac{39}{8}), Maximum (0, 5), Minimum (\frac{1}{2}, \frac{39}{8})

e x t re m e f (x) = 7 x^{9} - 9 x^{7} - 5 (- 3.4)

e x t re m e f (x) = - 3 + x^{2} - 3 x - 3 x^{3} + 2 x^{5} + 4 x^{4}

e x t re m e f (x) = - x^{3} + 6 x^{2} + 135 x + 1

e x t re m e x^{2} - 8 x + 15

e x t re m e x^{2} - 8 x + 13