extreme 4x^3+7x^2-20x+9

Lösung

extrempunkte

4 x^{3} + 7 x^{2} - 20 x + 9

Maximum (- 2, 45), Minimum (\frac{5}{6}, - \frac{53}{108})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} + 14 x - 20

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

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

Ansteigend

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

Stecke

x = - 2

4 x^{3} + 7 x^{2} - 20 x + 9 : 45

Maximum (- 2, 45)

Stecke

x = \frac{5}{6}

4 x^{3} + 7 x^{2} - 20 x + 9 : - \frac{53}{108}

Minimum (\frac{5}{6}, - \frac{53}{108})

Maximum (- 2, 45), Minimum (\frac{5}{6}, - \frac{53}{108})

a sy m pt o t es f (x) = \frac{x ^{3} - x ^{2} + x - 1}{x - x ^{3}}

in t erce pt s 3 x^{7} - x^{5} - 7 x^{4} - 2 x^{3} + 3 x^{2}

r an g e 2 x + 4 - 1

p a r a ll e l x + 3 y = 9

d o main f (x) = 3 x^{2} + 2 y^{2} = 48