extreme 10x^{1/2}-x[100]

Lösung

extrempunkte

10 x^{\frac{1}{2}} - x [100]

Maximum (0, 0), Minimum (\frac{1}{400}, \frac{1}{4})

Schritte zur Lösung

f^{'} (x) = \frac{5}{x ^{\frac{1}{2}}} - 100

Intervalle finden:

Absteigend

: 0 \leq x < 400,

Ansteigend

: 400 < x < \infty

Stecke

x = 0

10 x^{\frac{1}{2}} - x [100] : 0

Maximum (0, 0)

Stecke

x = \frac{1}{400}

10 x^{\frac{1}{2}} - x [100] : \frac{1}{4}

Minimum (\frac{1}{400}, \frac{1}{4})

Maximum (0, 0), Minimum (\frac{1}{400}, \frac{1}{4})

e x t re m e f (x) = 2 x^{3} - 2 x^{2} - 2 x + 6

e x t re m e f (x) = (4 x^{2} - 64)^{\frac{1}{5}}

e x t re m e f (x, y) = e^{y^{2} + x^{3} - 6 x y - 6 x + 2 y}

e x t re m e \frac{2 x + 4}{x ^{2} - 16}

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