extreme f(x)=sqrt(x)-\sqrt[3]{x}

Lösung

extrempunkte

f (x) = x - 3 x

Maximum (0, 0), Minimum (\frac{64}{729}, - \frac{4}{27})

Schritte zur Lösung

f^{'} (x) = \frac{1}{2 x} - \frac{1}{3 x ^{\frac{2}{3}}}

Intervalle finden:

Absteigend

: 0 < x < \frac{64}{729},

Ansteigend

: \frac{64}{729} < x < \infty

Stecke

x = 0

x - 3 x : 0

Maximum (0, 0)

Stecke

x = \frac{64}{729}

x - 3 x : - \frac{4}{27}

Minimum (\frac{64}{729}, - \frac{4}{27})

Maximum (0, 0), Minimum (\frac{64}{729}, - \frac{4}{27})

e x t re m e f (x) = ln (x^{2} + 7 x + 14), - 4 \leq x \leq 1

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e x t re m e f (x) = 2 x^{2} - 36 ln (x)

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

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