monotone f(x)=x^5-4x^3+2x

Lösung

monotone intervalle

f (x) = x^{5} - 4 x^{3} + 2 x

Ansteigend : - \infty < x < - \frac{6 + 26}{5}, Absteigend : - \frac{6 + 26}{5} < x < - \frac{6 - 26}{5}, Ansteigend : - \frac{6 - 26}{5} < x < \frac{6 - 26}{5}, Absteigend : \frac{6 - 26}{5} < x < \frac{6 + 26}{5}, Ansteigend : \frac{6 + 26}{5} < x < \infty

Schritte zur Lösung

f^{'} (x) = 5 x^{4} - 12 x^{2} + 2

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{6 + 26}{5},

Absteigend

: - \frac{6 + 26}{5} < x < - \frac{6 - 26}{5},

Ansteigend

: - \frac{6 - 26}{5} < x < \frac{6 - 26}{5},

Absteigend

: \frac{6 - 26}{5} < x < \frac{6 + 26}{5},

Ansteigend

: \frac{6 + 26}{5} < x < \infty

Ansteigend : - \infty < x < - \frac{6 + 26}{5}, Absteigend : - \frac{6 + 26}{5} < x < - \frac{6 - 26}{5}, Ansteigend : - \frac{6 - 26}{5} < x < \frac{6 - 26}{5}, Absteigend : \frac{6 - 26}{5} < x < \frac{6 + 26}{5}, Ansteigend : \frac{6 + 26}{5} < x < \infty