extreme f(x)=(x^2+4)/(8x)

Lösung

extrempunkte

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

Maximum (- 2, - \frac{1}{2}), Minimum (2, \frac{1}{2})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

\frac{x ^{2} + 4}{8 x} : - \frac{1}{2}

Maximum (- 2, - \frac{1}{2})

Stecke

x = 2

\frac{x ^{2} + 4}{8 x} : \frac{1}{2}

Minimum (2, \frac{1}{2})

Maximum (- 2, - \frac{1}{2}), Minimum (2, \frac{1}{2})

mi d p o in t (89, 43), (73, - 66)

m o n o t o n e f (x) = x^{2} + 6 x + 9

in t erce pt s f (x) = - 3 (x - 4)^{2} (x^{2} - 1)

d o main y = lo g_{10} (1 - x^{2})

v er t i ces y = 6 x^{2} - 12 x + 1