extreme-10x^4+4x^2-6

Lösung

extrempunkte

- 10 x^{4} + 4 x^{2} - 6

Maximum (- \frac{1}{5}, - \frac{28}{5}), Minimum (0, - 6), Maximum (\frac{1}{5}, - \frac{28}{5})

Schritte zur Lösung

f^{'} (x) = - 40 x^{3} + 8 x

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{5},

Absteigend

: - \frac{1}{5} < x < 0,

Ansteigend

: 0 < x < \frac{1}{5},

Absteigend

: \frac{1}{5} < x < \infty

Stecke

x = - \frac{1}{5}

- 10 x^{4} + 4 x^{2} - 6 : - \frac{28}{5}

Maximum (- \frac{1}{5}, - \frac{28}{5})

Stecke

x = 0

- 10 x^{4} + 4 x^{2} - 6 : - 6

Minimum (0, - 6)

Stecke

x = \frac{1}{5}

- 10 x^{4} + 4 x^{2} - 6 : - \frac{28}{5}

Maximum (\frac{1}{5}, - \frac{28}{5})

Maximum (- \frac{1}{5}, - \frac{28}{5}), Minimum (0, - 6), Maximum (\frac{1}{5}, - \frac{28}{5})

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

e x t re m e y = sin (x) cos (x)

e x t re m e f (x, y) = x^{3} + y^{3} + 7 x y

e x t re m e f (x) = 59.80 8^{2} - 11.148 x

e x t re m e f (x) = \frac{x ^{2} + 2}{x ^{2} - 16}