extreme f(x)=xsqrt(2-x)

Lösung

extrempunkte

f (x) = x 2 - x

Maximum (\frac{4}{3}, \frac{4 2}{3 3}), Minimum (2, 0)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{4}{3},

Absteigend

: \frac{4}{3} < x < 2

Stecke

x = \frac{4}{3}

x 2 - x : \frac{4 2}{3 3}

Maximum (\frac{4}{3}, \frac{4 2}{3 3})

Stecke

x = 2

x 2 - x : 0

Minimum (2, 0)

Maximum (\frac{4}{3}, \frac{4 2}{3 3}), Minimum (2, 0)

e x t re m e f (x, y, z) = x + y 2 + x 3

e x t re m e h (x) = - 3 x^{5} + 5 x^{3}

e x t re m e f (x) = ln (5 - 2 x^{2})

e x t re m e f (x) = 2 x^{3} - \frac{11}{2} x^{2} - 10 x + 2

e x t re m e f (x, y) = 8 y^{2} + 5 x^{2} - 10 y + 6 x - 10