extreme x^3-5x^2-x+4

Lösung

extrempunkte

x^{3} - 5 x^{2} - x + 4

Maximum (\frac{5 - 2 7}{3}, \frac{112 7 - 295}{27} + 4), Minimum (\frac{5 + 2 7}{3}, \frac{- 295 - 112 7}{27} + 4)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 10 x - 1

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 2 7 + 5}{3},

Absteigend

: \frac{- 2 7 + 5}{3} < x < \frac{2 7 + 5}{3},

Ansteigend

: \frac{2 7 + 5}{3} < x < \infty

Stecke

x = \frac{5 - 2 7}{3}

x^{3} - 5 x^{2} - x + 4 : \frac{112 7 - 295}{27} + 4

Maximum (\frac{5 - 2 7}{3}, \frac{112 7 - 295}{27} + 4)

Stecke

x = \frac{5 + 2 7}{3}

x^{3} - 5 x^{2} - x + 4 : \frac{- 295 - 112 7}{27} + 4

Minimum (\frac{5 + 2 7}{3}, \frac{- 295 - 112 7}{27} + 4)

Maximum (\frac{5 - 2 7}{3}, \frac{112 7 - 295}{27} + 4), Minimum (\frac{5 + 2 7}{3}, \frac{- 295 - 112 7}{27} + 4)

s l o p e y = 4 x + 2

d o main f (x) = 3 x^{2} + 2 x^{4} - 2

s l o p e f (x) = 5

d o main 2 x - 4

d o main f (x) = \frac{5 ( x + 5 )}{x}