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

Lösung

monotone intervalle

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

Absteigend : - \infty < x < - 1, Ansteigend : - 1 < x < - \frac{1}{2}, Absteigend : - \frac{1}{2} < x < 0, Ansteigend : 0 < x < \infty

Schritte zur Lösung

f^{'} (x) = 4 x^{3} + 6 x^{2} + 2 x

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < - \frac{1}{2},

Absteigend

: - \frac{1}{2} < x < 0,

Ansteigend

: 0 < x < \infty

Absteigend : - \infty < x < - 1, Ansteigend : - 1 < x < - \frac{1}{2}, Absteigend : - \frac{1}{2} < x < 0, Ansteigend : 0 < x < \infty

d o main \frac{2}{\frac{x}{x + 2}}

in t erce pt s f (x) = x^{2} + x - 12

y = - 0.23 x^{2} + 1.87 x + 1.5

a sy m pt o t es f (x) = x e^{- 8 x}

p a r a ll e l y = y + 4, at 2, 2