extreme f(x)=16x+9x^{-1}

Lösung

extrempunkte

f (x) = 16 x + 9 x^{- 1}

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

Schritte zur Lösung

f^{'} (x) = 16 - \frac{9}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{4},

Absteigend

: - \frac{3}{4} < x < 0,

Absteigend

: 0 < x < \frac{3}{4},

Ansteigend

: \frac{3}{4} < x < \infty

Stecke

x = - \frac{3}{4}

16 x + 9 x^{- 1} : - 24

Maximum (- \frac{3}{4}, - 24)

Stecke

x = \frac{3}{4}

16 x + 9 x^{- 1} : 24

Minimum (\frac{3}{4}, 24)

Maximum (- \frac{3}{4}, - 24), Minimum (\frac{3}{4}, 24)

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

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

e x t re m e f (x) = \frac{x ^{2} - 7}{x + 4}

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

e x t re m e f (x) = 4 x - x