extreme 6x^4-7x^2-5

Lösung

extrempunkte

6 x^{4} - 7 x^{2} - 5

Minimum (- \frac{7}{2 3}, - \frac{169}{24}), Maximum (0, - 5), Minimum (\frac{7}{2 3}, - \frac{169}{24})

Schritte zur Lösung

f^{'} (x) = 24 x^{3} - 14 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{7}{2 3},

Ansteigend

: - \frac{7}{2 3} < x < 0,

Absteigend

: 0 < x < \frac{7}{2 3},

Ansteigend

: \frac{7}{2 3} < x < \infty

Stecke

x = - \frac{7}{2 3}

6 x^{4} - 7 x^{2} - 5 : - \frac{169}{24}

Minimum (- \frac{7}{2 3}, - \frac{169}{24})

Stecke

x = 0

6 x^{4} - 7 x^{2} - 5 : - 5

Maximum (0, - 5)

Stecke

x = \frac{7}{2 3}

6 x^{4} - 7 x^{2} - 5 : - \frac{169}{24}

Minimum (\frac{7}{2 3}, - \frac{169}{24})

Minimum (- \frac{7}{2 3}, - \frac{169}{24}), Maximum (0, - 5), Minimum (\frac{7}{2 3}, - \frac{169}{24})

a sy m pt o t es \frac{x ^{3} - x ^{2}}{x ^{3} - 3 x - 2}

e x t re m e f (x) = \frac{x ^{2} - 15}{x - 4}

d o main f (x) = x + 5 - x

in v erse f (x) = ln (x - 3)

in f l ec t i o n \frac{3 x ^{4} + 1}{x ^{3}}