extreme f(x)=((15/4)x)+(5x^3)-(90x^2)+15

Lösung

extrempunkte

f (x) = ((\frac{15}{4}) x) + (5 x^{3}) - (90 x^{2}) + 15

Maximum (\frac{12 - 143}{2}, \frac{715 143 - 8550}{4} + 15), Minimum (\frac{12 + 143}{2}, \frac{- 8550 - 715 143}{4} + 15)

Schritte zur Lösung

f^{'} (x) = 15 x^{2} - 180 x + \frac{15}{4}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{143}{2} + 6,

Absteigend

: - \frac{143}{2} + 6 < x < \frac{143}{2} + 6,

Ansteigend

: \frac{143}{2} + 6 < x < \infty

Stecke

x = \frac{12 - 143}{2}

\frac{15}{4} x + 5 x^{3} - 90 x^{2} + 15 : \frac{715 143 - 8550}{4} + 15

Maximum (\frac{12 - 143}{2}, \frac{715 143 - 8550}{4} + 15)

Stecke

x = \frac{12 + 143}{2}

\frac{15}{4} x + 5 x^{3} - 90 x^{2} + 15 : \frac{- 8550 - 715 143}{4} + 15

Minimum (\frac{12 + 143}{2}, \frac{- 8550 - 715 143}{4} + 15)

Maximum (\frac{12 - 143}{2}, \frac{715 143 - 8550}{4} + 15), Minimum (\frac{12 + 143}{2}, \frac{- 8550 - 715 143}{4} + 15)

e x t re m e f (x, y) = 1 + e^{(x^{2} + y^{2})}

e x t re m e A (3, - 5) B (1, - 2)

e x t re m e f (x) = 518 x - 3 x^{2} - 100 - 50 x

e x t re m e 3 x^{2} y + y^{3} - 3 y

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