extreme f(x)=8x+7x^{-1}

Lösung

extrempunkte

f (x) = 8 x + 7 x^{- 1}

Maximum (- \frac{7}{2 2}, - 414), Minimum (\frac{7}{2 2}, 414)

Schritte zur Lösung

f^{'} (x) = 8 - \frac{7}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7}{2 2},

Absteigend

: - \frac{7}{2 2} < x < 0,

Absteigend

: 0 < x < \frac{7}{2 2},

Ansteigend

: \frac{7}{2 2} < x < \infty

Stecke

x = - \frac{7}{2 2}

8 x + 7 x^{- 1} : - 414

Maximum (- \frac{7}{2 2}, - 414)

Stecke

x = \frac{7}{2 2}

8 x + 7 x^{- 1} : 414

Minimum (\frac{7}{2 2}, 414)

Maximum (- \frac{7}{2 2}, - 414), Minimum (\frac{7}{2 2}, 414)

e x t re m e f (x) = x^{3} + 6 x^{2} + 12 x + 7

e x t re m e f (p, q) = 3 p^{3} + 4 q^{3} - 2 p^{2} q - 4 p - 5 q

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

e x t re m e f (x, y) = 2 x^{2} + 2 x y + 2 y^{2} - 6 x

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