extreme f(x)=5x+9x^{-1}

Lösung

extrempunkte

f (x) = 5 x + 9 x^{- 1}

Maximum (- \frac{3}{5}, - 65), Minimum (\frac{3}{5}, 65)

Schritte zur Lösung

f^{'} (x) = 5 - \frac{9}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{5},

Absteigend

: - \frac{3}{5} < x < 0,

Absteigend

: 0 < x < \frac{3}{5},

Ansteigend

: \frac{3}{5} < x < \infty

Stecke

x = - \frac{3}{5}

5 x + 9 x^{- 1} : - 65

Maximum (- \frac{3}{5}, - 65)

Stecke

x = \frac{3}{5}

5 x + 9 x^{- 1} : 65

Minimum (\frac{3}{5}, 65)

Maximum (- \frac{3}{5}, - 65), Minimum (\frac{3}{5}, 65)

e x t re m e P (x, y) = 2 x^{2} - x y - 3 y^{2}

e x t re m e x^{4} + (1 - x)^{4} + 10 x^{2} (1 - x)^{2}

e x t re m e - 7 x + 6

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

e x t re m e f (x) = cos (x) - 5 x