extreme f(x)= x/(x^2+64)

Lösung

extrempunkte

f (x) = \frac{x}{x ^{2} + 64}

Minimum (- 8, - \frac{1}{16}), Maximum (8, \frac{1}{16})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 64}{( x ^{2} + 64 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 8,

Ansteigend

: - 8 < x < 8,

Absteigend

: 8 < x < \infty

Stecke

x = - 8

\frac{x}{x ^{2} + 64} : - \frac{1}{16}

Minimum (- 8, - \frac{1}{16})

Stecke

x = 8

\frac{x}{x ^{2} + 64} : \frac{1}{16}

Maximum (8, \frac{1}{16})

Minimum (- 8, - \frac{1}{16}), Maximum (8, \frac{1}{16})

d o main f (x) = x + 1 - x

r an g e (x + 2)^{\frac{1}{2}}

d o main f (x) = \frac{( \frac{x}{x + 8} )}{( \frac{x}{x + 8} ) + 8}

d o main - 2 (x + 1)^{2} (x - 4)^{3} (x + 2)

d o main y = \frac{x + 8}{x - 7}