extreme f(x)=-5x^3+25x^2+15

Lösung

extrempunkte

f (x) = - 5 x^{3} + 25 x^{2} + 15

Minimum (0, 15), Maximum (\frac{10}{3}, \frac{2905}{27})

Schritte zur Lösung

f^{'} (x) = - 15 x^{2} + 50 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{10}{3},

Absteigend

: \frac{10}{3} < x < \infty

Stecke

x = 0

- 5 x^{3} + 25 x^{2} + 15 : 15

Minimum (0, 15)

Stecke

x = \frac{10}{3}

- 5 x^{3} + 25 x^{2} + 15 : \frac{2905}{27}

Maximum (\frac{10}{3}, \frac{2905}{27})

Minimum (0, 15), Maximum (\frac{10}{3}, \frac{2905}{27})

in v erse g (x) = x - 25

p a r a ll e l y = - 7 x + 21

d i s t an ce (\frac{16}{3}, \frac{1}{5}), (\frac{1}{3}, \frac{6}{5})

s hi f t - 3 sin (x - \frac{π}{4})

a sy m pt o t es lo g_{7} (- x)