extreme f(x)=7x^4-6x^2-1

Lösung

extrempunkte

f (x) = 7 x^{4} - 6 x^{2} - 1

Minimum (- \frac{3}{7}, - \frac{16}{7}), Maximum (0, - 1), Minimum (\frac{3}{7}, - \frac{16}{7})

Schritte zur Lösung

f^{'} (x) = 28 x^{3} - 12 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{7},

Ansteigend

: - \frac{3}{7} < x < 0,

Absteigend

: 0 < x < \frac{3}{7},

Ansteigend

: \frac{3}{7} < x < \infty

Stecke

x = - \frac{3}{7}

7 x^{4} - 6 x^{2} - 1 : - \frac{16}{7}

Minimum (- \frac{3}{7}, - \frac{16}{7})

Stecke

x = 0

7 x^{4} - 6 x^{2} - 1 : - 1

Maximum (0, - 1)

Stecke

x = \frac{3}{7}

7 x^{4} - 6 x^{2} - 1 : - \frac{16}{7}

Minimum (\frac{3}{7}, - \frac{16}{7})

Minimum (- \frac{3}{7}, - \frac{16}{7}), Maximum (0, - 1), Minimum (\frac{3}{7}, - \frac{16}{7})

e x t re m e x^{2} - 2 x y + y^{3} - y

e x t re m e f (x) = 4 x + \frac{4}{x}

e x t re m e f (x) = 7 x^{4} - 6 x^{2} - 6

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

e x t re m e 2 x^{5} - 15 x^{4} + 30 x^{3} - 6