extreme y=x^4-9x^2

Lösung

extrempunkte

y = x^{4} - 9 x^{2}

Minimum (- \frac{3}{2}, - \frac{81}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{81}{4})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 18 x

Intervalle finden:

Absteigend

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

Ansteigend

: - \frac{3}{2} < x < 0,

Absteigend

: 0 < x < \frac{3}{2},

Ansteigend

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

Stecke

x = - \frac{3}{2}

x^{4} - 9 x^{2} : - \frac{81}{4}

Minimum (- \frac{3}{2}, - \frac{81}{4})

Stecke

x = 0

x^{4} - 9 x^{2} : 0

Maximum (0, 0)

Stecke

x = \frac{3}{2}

x^{4} - 9 x^{2} : - \frac{81}{4}

Minimum (\frac{3}{2}, - \frac{81}{4})

Minimum (- \frac{3}{2}, - \frac{81}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{81}{4})

d o main y = \frac{1}{x - 2}

d o main y = e^{x - 2}

a sy m pt o t es \frac{x ^{2} + 6}{- 2 x + 1}

in v erse f (x) = \frac{e ^{x}}{1 + e ^{x}}

d o main f (x) = \frac{x ^{2} - 1}{x ^{2} + 1}