extreme f(x)=3x^4-20x^3+24x^2

Lösung

extrempunkte

f (x) = 3 x^{4} - 20 x^{3} + 24 x^{2}

Minimum (0, 0), Maximum (1, 7), Minimum (4, - 128)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 60 x^{2} + 48 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

3 x^{4} - 20 x^{3} + 24 x^{2} : 0

Minimum (0, 0)

Stecke

x = 1

3 x^{4} - 20 x^{3} + 24 x^{2} : 7

Maximum (1, 7)

Stecke

x = 4

3 x^{4} - 20 x^{3} + 24 x^{2} : - 128

Minimum (4, - 128)

Minimum (0, 0), Maximum (1, 7), Minimum (4, - 128)

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

s im pl i f y (1.7) (- 8.3)

d o main f (x) = \frac{x + 7}{x - 8}

m o n o t o n e f (x) = \frac{x + 3}{x ^{2}}

p a r i t y f (x) = x + e^{x}