extreme f(x)=(x-3)(x+1)(x+4)

Lösung

extrempunkte

f (x) = (x - 3) (x + 1) (x + 4)

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10), Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} + 4 x - 11

Intervalle finden:

Ansteigend

: - \infty < x < \frac{- 37 - 2}{3},

Absteigend

: \frac{- 37 - 2}{3} < x < \frac{37 - 2}{3},

Ansteigend

: \frac{37 - 2}{3} < x < \infty

Stecke

x = - \frac{2 + 37}{3}

(x - 3) (x + 1) (x + 4) : \frac{160 + 47 37}{27} + 37 - 10

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10)

Stecke

x = \frac{- 2 + 37}{3}

(x - 3) (x + 1) (x + 4) : \frac{160 - 47 37}{27} - 10 - 37

Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10), Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

e x t re m e f (x) = 3 x^{2} - 4 y^{3} - 6 x + 48 y - 1

e x t re m e f (x) = x^{2} + y^{2} - 8 x + y

e x t re m e f (x) = 3 x^{2} + 6 x - 6

e x t re m e f (x) = - x^{3} - x^{2} + 5 x + 1

e x t re m e \frac{30}{x} + 3 π x^{2}