extreme f(x)=-13t^3+18t^2+37t+6

Lösung

extrempunkte

f (x) = - 13 t^{3} + 18 t^{2} + 37 t + 6

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6), Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

Schritte zur Lösung

f^{'} (t) = - 39 t^{2} + 36 t + 37

Intervalle finden:

Absteigend

: - \infty < t < - \frac{589}{13 3} + \frac{6}{13},

Ansteigend

: - \frac{589}{13 3} + \frac{6}{13} < t < \frac{589}{13 3} + \frac{6}{13},

Absteigend

: \frac{589}{13 3} + \frac{6}{13} < t < \infty

Stecke

t = - \frac{- 18 + 1767}{39}

- 13 t^{3} + 18 t^{2} + 37 t + 6 : \frac{29862 - 1178 1767}{1521} + 6

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6)

Stecke

t = \frac{18 + 1767}{39}

- 13 t^{3} + 18 t^{2} + 37 t + 6 : \frac{29862 + 1178 1767}{1521} + 6

Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6), Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

e x t re m e y = \frac{6 x}{x ^{2} - 9}

e x t re m e f (x) = \frac{2 x - 3}{x ^{2} - 3 x} se

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

e x t re m e f (x, y) = 9 x^{2} y - 9 x y^{3} + 9 y^{3}

e x t re m e f (x, y) = 3 x^{2} - 5 x y + 6 y^{2} + x - y