extreme f(x)=36x+9/x

Lösung

extrempunkte

f (x) = 36 x + \frac{9}{x}

Maximum (- \frac{1}{2}, - 36), Minimum (\frac{1}{2}, 36)

Schritte zur Lösung

f^{'} (x) = 36 - \frac{9}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{2},

Absteigend

: - \frac{1}{2} < x < 0,

Absteigend

: 0 < x < \frac{1}{2},

Ansteigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{1}{2}

36 x + \frac{9}{x} : - 36

Maximum (- \frac{1}{2}, - 36)

Stecke

x = \frac{1}{2}

36 x + \frac{9}{x} : 36

Minimum (\frac{1}{2}, 36)

Maximum (- \frac{1}{2}, - 36), Minimum (\frac{1}{2}, 36)

d o main f (x) = \frac{1}{x ^{2} - x - 90}

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

d o main f (x) = \frac{x + 7}{x ^{2} - x - 56}

s l o p e in t erce pt 0.5 \cdot 80 + 25

in v erse f (x) = 65