extreme f(x)=(3x-1)(x+3)(x-2)

Lösung

extrempunkte

f (x) = (3 x - 1) (x + 3) (x - 2)

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10), Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

Schritte zur Lösung

f^{'} (x) = 9 x^{2} + 4 x - 19

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 5 7 - 2}{9},

Absteigend

: \frac{- 5 7 - 2}{9} < x < \frac{5 7 - 2}{9},

Ansteigend

: \frac{5 7 - 2}{9} < x < \infty

Stecke

x = - \frac{2 + 5 7}{9}

(3 x - 1) (x + 3) (x - 2) : 107 + \frac{70 - 680 7}{243} + 10

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10)

Stecke

x = \frac{- 2 + 5 7}{9}

(3 x - 1) (x + 3) (x - 2) : - 107 + \frac{70 + 680 7}{243} + 10

Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10), Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

p er p e n d i c u l a r x - 2 y = 6

in v erse f (x) = \frac{x - 3}{x + 9}

p a r i t y f (x) = \frac{1}{x ^{2} - 5 x + 6}

d o main f (x) = - 3 x - 2

in v erse f (x) = 1 1^{x}