extreme f(x)=x(20-43+2x)(43/2-x)

Lösung

extrempunkte

f (x) = x (20 - 43 + 2 x) (\frac{43}{2} - x)

Minimum (\frac{66 - 1389}{6}, - \frac{2079 + 463 1389}{18}), Maximum (\frac{66 + 1389}{6}, \frac{463 1389 - 2079}{18})

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 132 x - \frac{989}{2}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{463}{2 3} + 11,

Ansteigend

: - \frac{463}{2 3} + 11 < x < \frac{463}{2 3} + 11,

Absteigend

: \frac{463}{2 3} + 11 < x < \infty

Stecke

x = \frac{66 - 1389}{6}

x (20 - 43 + 2 x) (\frac{43}{2} - x) : - \frac{2079 + 463 1389}{18}

Minimum (\frac{66 - 1389}{6}, - \frac{2079 + 463 1389}{18})

Stecke

x = \frac{66 + 1389}{6}

x (20 - 43 + 2 x) (\frac{43}{2} - x) : \frac{463 1389 - 2079}{18}

Maximum (\frac{66 + 1389}{6}, \frac{463 1389 - 2079}{18})

Minimum (\frac{66 - 1389}{6}, - \frac{2079 + 463 1389}{18}), Maximum (\frac{66 + 1389}{6}, \frac{463 1389 - 2079}{18})

e x t re m e x^{4} - 2 x^{2} - 2

e x t re m e x^{4} - 2 x^{2} + 1

e x t re m e y = 63 x + 12 cos (x)

e x t re m e f (x, y) = x^{2} + 7 y^{2} + x - 6 y + 4

e x t re m e f (x) = 2 x^{2} ln (x) - 19 x^{2}