extreme 4h^3-96h^2+527h

Lösung

extrempunkte

4 h^{3} - 96 h^{2} + 527 h

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}), Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

Schritte zur Lösung

f^{'} (h) = 12 h^{2} - 192 h + 527

Intervalle finden:

Ansteigend

: - \infty < h < - \frac{241}{2 3} + 8,

Absteigend

: - \frac{241}{2 3} + 8 < h < \frac{241}{2 3} + 8,

Ansteigend

: \frac{241}{2 3} + 8 < h < \infty

Stecke

h = \frac{48 - 723}{6}

4 h^{3} - 96 h^{2} + 527 h : - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9})

Stecke

h = \frac{48 + 723}{6}

4 h^{3} - 96 h^{2} + 527 h : - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9}

Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}), Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

e x t re m e f (x) = 25 x^{2} - 25 y^{2} + 200 x + 200 y + 200

e x t re m e x^{2} + y^{2} + 6 x - 10 y + 5

e x t re m e y = - 5 x^{3} + 4 x^{2} + 5 x - 1

e x t re m e f (x) = \frac{9 x ^{2} - 1}{x}

e x t re m e y = 5 + 12 x^{2} - 8 x^{3}