extreme f(t)=108t-t^3

Lösung

extrempunkte

f (t) = 108 t - t^{3}

Minimum (- 6, - 432), Maximum (6, 432)

Schritte zur Lösung

f^{'} (t) = 108 - 3 t^{2}

Intervalle finden:

Absteigend

: - \infty < t < - 6,

Ansteigend

: - 6 < t < 6,

Absteigend

: 6 < t < \infty

Stecke

t = - 6

108 t - t^{3} : - 432

Minimum (- 6, - 432)

Stecke

t = 6

108 t - t^{3} : 432

Maximum (6, 432)

Minimum (- 6, - 432), Maximum (6, 432)

e x t re m e f (x) = 2 x^{3} + 6 x^{2} - 90 x + 1, - 5 \leq x \leq 7

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

e x t re m e \frac{1}{2 π} e^{- (x - 3)^{\frac{2}{2}}}

e x t re m e f (x) = 4 (e^{- 0.05 x} - e^{- 0.55 x})

e x t re m e f (x) = - x^{3} + 1.5 x^{2} + 36 x + 2