extreme 4x^2-8x^4

Lösung

extrempunkte

4 x^{2} - 8 x^{4}

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

Schritte zur Lösung

f^{'} (x) = 8 x - 32 x^{3}

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

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

Absteigend

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

Stecke

x = - \frac{1}{2}

4 x^{2} - 8 x^{4} : \frac{1}{2}

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

Stecke

x = 0

4 x^{2} - 8 x^{4} : 0

Minimum (0, 0)

Stecke

x = \frac{1}{2}

4 x^{2} - 8 x^{4} : \frac{1}{2}

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

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

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

e x t re m e f (x) = 9 x^{3} + 21 x^{2} + 8 x - 3

e x t re m e f (x) = x^{2} - 2 x + 5 [- 1.4]

e x t re m e 2 x^{4} - 196 x^{2} - 3

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