extreme f(t)=3t+1/t

Lösung

extrempunkte

f (t) = 3 t + \frac{1}{t}

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

Schritte zur Lösung

f^{'} (t) = 3 - \frac{1}{t ^{2}}

Intervalle finden:

Ansteigend

: - \infty < t < - \frac{1}{3},

Absteigend

: - \frac{1}{3} < t < 0,

Absteigend

: 0 < t < \frac{1}{3},

Ansteigend

: \frac{1}{3} < t < \infty

Stecke

t = - \frac{1}{3}

3 t + \frac{1}{t} : - 23

Maximum (- \frac{1}{3}, - 23)

Stecke

t = \frac{1}{3}

3 t + \frac{1}{t} : 23

Minimum (\frac{1}{3}, 23)

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

e x t re m e f (x) = \frac{9}{2} x^{2} - ln (x)

e x t re m e f (x) = 3 x + 1

e x t re m e f (x) = \frac{5 ( x - 6 ) ^{2}}{x - 1}

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

e x t re m e f (x) = x^{3} - x^{2} - 8 x + 12