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Beliebt Funktionen >

extreme f(x)=(3x+1)^5(2x+3)^2(2-x)^3

Lösung

extrempunkte

f (x) = (3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3}

Lösung

Maximum (- \frac{3}{2}, 0), Minimum (\frac{1 - 7 109}{60}, \frac{136600387 109 - 1318618861}{12150000} + \frac{5.72682 E 17 - 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 - 637 109 )}{225} + 72), Sattel (- \frac{1}{3}, 0), Maximum (\frac{1 + 7 109}{60}, \frac{- 1318618861 - 136600387 109}{12150000} + \frac{5.72682 E 17 + 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 + 637 109 )}{225} + 72), Sattel (2, 0)

Schritte zur Lösung

f^{'} (x) = - (1 + 3 x)^{4} (x - 2)^{2} (2 x + 3) (60 x^{2} - 2 x - 89)

Intervalle finden:

Ansteigend

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

Absteigend

: - \frac{3}{2} < x < \frac{1 - 7 109}{60},

Ansteigend

: \frac{1 - 7 109}{60} < x < - \frac{1}{3},

Ansteigend

: - \frac{1}{3} < x < \frac{1 + 7 109}{60},

Absteigend

: \frac{1 + 7 109}{60} < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - \frac{3}{2}

in

(3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3} : 0

Maximum (- \frac{3}{2}, 0)

Stecke

x = \frac{1 - 7 109}{60}

in

(3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3} : \frac{136600387 109 - 1318618861}{12150000} + \frac{5.72682 E 17 - 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 - 637 109 )}{225} + 72

Minimum (\frac{1 - 7 109}{60}, \frac{136600387 109 - 1318618861}{12150000} + \frac{5.72682 E 17 - 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 - 637 109 )}{225} + 72)

Stecke

x = - \frac{1}{3}

in

(3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3} : 0

Sattel (- \frac{1}{3}, 0)

Stecke

x = \frac{1 + 7 109}{60}

in

(3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3} : \frac{- 1318618861 - 136600387 109}{12150000} + \frac{5.72682 E 17 + 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 + 637 109 )}{225} + 72

Maximum (\frac{1 + 7 109}{60}, \frac{- 1318618861 - 136600387 109}{12150000} + \frac{5.72682 E 17 + 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 + 637 109 )}{225} + 72)

Stecke

x = 2

in

(3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3} : 0

Sattel (2, 0)

Maximum (- \frac{3}{2}, 0), Minimum (\frac{1 - 7 109}{60}, \frac{136600387 109 - 1318618861}{12150000} + \frac{5.72682 E 17 - 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 - 637 109 )}{225} + 72), Sattel (- \frac{1}{3}, 0), Maximum (\frac{1 + 7 109}{60}, \frac{- 1318618861 - 136600387 109}{12150000} + \frac{5.72682 E 17 + 6.01163 E 16 109}{3.888 E 13} + \frac{4 ( 2761 + 637 109 )}{225} + 72), Sattel (2, 0)

Graph

Beliebte Beispiele

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