extreme f(x)= x/(49+x^2)

Lösung

extrempunkte

f (x) = \frac{x}{49 + x ^{2}}

Minimum (- 7, - \frac{1}{14}), Maximum (7, \frac{1}{14})

Schritte zur Lösung

f^{'} (x) = \frac{49 - x ^{2}}{( 49 + x ^{2} ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 7,

Ansteigend

: - 7 < x < 7,

Absteigend

: 7 < x < \infty

Stecke

x = - 7

\frac{x}{49 + x ^{2}} : - \frac{1}{14}

Minimum (- 7, - \frac{1}{14})

Stecke

x = 7

\frac{x}{49 + x ^{2}} : \frac{1}{14}

Maximum (7, \frac{1}{14})

Minimum (- 7, - \frac{1}{14}), Maximum (7, \frac{1}{14})

p a r i t y f (x) = 3 x + 1

d o main f (x) = 25 - x^{2} + x + 3

p er i o d i c i t y f (x) = 6 sin (3 x)

cr i t i c a l \frac{x ^{3} - 4 x}{1 + x ^{2}}

d o main f (x) = lo g_{2} (x + 1)