extreme-4x^4+3x^3+3x^2

Lösung

extrempunkte

- 4 x^{4} + 3 x^{3} + 3 x^{2}

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768}), Minimum (0, 0), Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

Schritte zur Lösung

f^{'} (x) = - 16 x^{3} + 9 x^{2} + 6 x

Intervalle finden:

Ansteigend

: - \infty < x < \frac{9 - 465}{32},

Absteigend

: \frac{9 - 465}{32} < x < 0,

Ansteigend

: 0 < x < \frac{9 + 465}{32},

Absteigend

: \frac{9 + 465}{32} < x < \infty

Stecke

x = \frac{9 - 465}{32}

- 4 x^{4} + 3 x^{3} + 3 x^{2} : \frac{9 ( 4019 - 155 465 )}{32768}

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768})

Stecke

x = 0

- 4 x^{4} + 3 x^{3} + 3 x^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{9 + 465}{32}

- 4 x^{4} + 3 x^{3} + 3 x^{2} : \frac{9 ( 4019 + 155 465 )}{32768}

Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768}), Minimum (0, 0), Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

d i s t an ce (- 4, 2), (2, 4)

d o main f (x) = \frac{x ^{2} + 1 + 8 x}{x ^{2} + 1 + 2 x}

in t erce pt s f (x) = x^{2} - 2 x + 3

in f l ec t i o n f (x) = - x^{2} + 8 x + 8

a sy m pt o t es \frac{x ^{2} + x + 1}{x}