extreme 6x^5+33x^4-30x^3+100

Lösung

extrempunkte

6 x^{5} + 33 x^{4} - 30 x^{3} + 100

Maximum (- 5, 5725), Sattel (0, 100), Minimum (\frac{3}{5}, \frac{307073}{3125})

Schritte zur Lösung

f^{'} (x) = 30 x^{4} + 132 x^{3} - 90 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 5,

Absteigend

: - 5 < x < 0,

Absteigend

: 0 < x < \frac{3}{5},

Ansteigend

: \frac{3}{5} < x < \infty

Stecke

x = - 5

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : 5725

Maximum (- 5, 5725)

Stecke

x = 0

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : 100

Sattel (0, 100)

Stecke

x = \frac{3}{5}

6 x^{5} + 33 x^{4} - 30 x^{3} + 100 : \frac{307073}{3125}

Minimum (\frac{3}{5}, \frac{307073}{3125})

Maximum (- 5, 5725), Sattel (0, 100), Minimum (\frac{3}{5}, \frac{307073}{3125})

e x t re m e f (x, y) = x^{2} + y^{2} - 10

e x t re m e f (x) = \frac{( x + 1 )}{x ^{2} + x + 1}

e x t re m e f (x) = x, 0 \leq x \leq 16

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

e x t re m e f (x) = 2 x^{3} - 24 x^{2} + 72 x + 10