extreme y=xsqrt(4-x)

Lösung

extrempunkte

y = x 4 - x

Maximum (\frac{8}{3}, \frac{16}{3 3}), Minimum (4, 0)

Schritte zur Lösung

f^{'} (x) = \frac{- 3 x + 8}{2 4 - x}

Intervalle finden:

Ansteigend

: - \infty < x < \frac{8}{3},

Absteigend

: \frac{8}{3} < x < 4

Stecke

x = \frac{8}{3}

x 4 - x : \frac{16}{3 3}

Maximum (\frac{8}{3}, \frac{16}{3 3})

Stecke

x = 4

x 4 - x : 0

Minimum (4, 0)

Maximum (\frac{8}{3}, \frac{16}{3 3}), Minimum (4, 0)

e x t re m e f (x) = (3 x + 1)^{5} (2 x + 3)^{2} (2 - x)^{3}

e x t re m e y = 2 x^{3} - 12 x^{2} - 270 x + 2

e x t re m e y = 0.0004 x^{2} - 0.0118 x + 2.6821

e x t re m e x (\frac{8}{5} x^{3} - 2 x^{2})

e x t re m e f (x) = ln (\frac{4 - x}{2 + 2 x})