extreme f(x)= x/(x^2+14x+48)

Lösung

extrempunkte

f (x) = \frac{x}{x ^{2} + 14 x + 48}

Minimum (- 43, \frac{7 + 4 3}{2}), Maximum (43, \frac{7 - 4 3}{2})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 48}{( x ^{2} + 14 x + 48 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 8,

Absteigend

: - 8 < x < - 43,

Ansteigend

: - 43 < x < - 6,

Ansteigend

: - 6 < x < 43,

Absteigend

: 43 < x < \infty

Stecke

x = - 43

\frac{x}{x ^{2} + 14 x + 48} : \frac{7 + 4 3}{2}

Minimum (- 43, \frac{7 + 4 3}{2})

Stecke

x = 43

\frac{x}{x ^{2} + 14 x + 48} : \frac{7 - 4 3}{2}

Maximum (43, \frac{7 - 4 3}{2})

Minimum (- 43, \frac{7 + 4 3}{2}), Maximum (43, \frac{7 - 4 3}{2})

e x t re m e f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 1

e x t re m e f (x) = 2 x^{2} - 100 ln (x)

e x t re m e ∣ sin (x) ∣

e x t re m e f (x) = 2 x^{3} + 3 x^{2} - 36 x + 4

e x t re m e f (x) = x^{2} - 4 x y + 5