extreme f(x)=(x^2-3)(x^{1/2})

Lösung

extrempunkte

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

Maximum (0, 0), Minimum ((\frac{3}{5})^{\frac{1}{2}}, - \frac{12 \cdot 3 ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}})

Schritte zur Lösung

f^{'} (x) = \frac{( 5 ^{\frac{1}{2}} x + 3 ^{\frac{1}{2}} ) ( 5 ^{\frac{1}{2}} x - 3 ^{\frac{1}{2}} )}{2 x ^{\frac{1}{2}}}

Intervalle finden:

Absteigend

: 0 < x < (\frac{3}{5})^{\frac{1}{2}},

Ansteigend

: (\frac{3}{5})^{\frac{1}{2}} < x < \infty

Stecke

x = 0

(x^{2} - 3) x^{\frac{1}{2}} : 0

Maximum (0, 0)

Stecke

x = (\frac{3}{5})^{\frac{1}{2}}

(x^{2} - 3) x^{\frac{1}{2}} : - \frac{12 \cdot 3 ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}}

Minimum ((\frac{3}{5})^{\frac{1}{2}}, - \frac{12 \cdot 3 ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}})

Maximum (0, 0), Minimum ((\frac{3}{5})^{\frac{1}{2}}, - \frac{12 \cdot 3 ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}})

p er i o d i c i t y f (x) = sin (20 π t)

in t erce pt s f (x) = - x^{2} + 9

sy mm e t ry x^{2} - 5 x + 4

in v erse f (x) = - \frac{2}{x + 1} + 3

p er p e n d i c u l a r y = 9 x - 6