extreme f(x)= 2/3 x^3-4x^2-45x

Lösung

extrempunkte

f (x) = \frac{2}{3} x^{3} - 4 x^{2} - 45 x

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3}), Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

Schritte zur Lösung

f^{'} (x) = 2 x^{2} - 8 x - 45

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{53}{2} + 2,

Absteigend

: - \frac{53}{2} + 2 < x < \frac{53}{2} + 2,

Ansteigend

: \frac{53}{2} + 2 < x < \infty

Stecke

x = \frac{4 - 106}{2}

\frac{2}{3} x^{3} - 4 x^{2} - 45 x : - 2 (61 - 4106) + \frac{64 + 29 106}{3}

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3})

Stecke

x = \frac{4 + 106}{2}

\frac{2}{3} x^{3} - 4 x^{2} - 45 x : - 2 (61 + 4106) + \frac{64 - 29 106}{3}

Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3}), Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 37 y + 456

e x t re m e f (x, y) = 3 x^{2} - y^{2}

e x t re m e 3 x^{5} - 5 x^{3} + 1

e x t re m e f (x) = 2 x^{2} + 3 x y + 4 y^{2} - 2 x + 10 y

e x t re m e f (x) = x^{4} - 8 x^{3} - 6