extreme f(x)=((x^2+12))/(x-3)

Lösung

extrempunkte

f (x) = \frac{( x ^{2} + 12 )}{x - 3}

Maximum (3 - 21, - \frac{14 3 - 6 7}{7}), Minimum (3 + 21, \frac{14 3 + 6 7}{7})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 6 x - 12}{( x - 3 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 3 - 21,

Absteigend

: 3 - 21 < x < 3,

Absteigend

: 3 < x < 3 + 21,

Ansteigend

: 3 + 21 < x < \infty

Stecke

x = 3 - 21

\frac{x ^{2} + 12}{x - 3} : - \frac{14 3 - 6 7}{7}

Maximum (3 - 21, - \frac{14 3 - 6 7}{7})

Stecke

x = 3 + 21

\frac{x ^{2} + 12}{x - 3} : \frac{14 3 + 6 7}{7}

Minimum (3 + 21, \frac{14 3 + 6 7}{7})

Maximum (3 - 21, - \frac{14 3 - 6 7}{7}), Minimum (3 + 21, \frac{14 3 + 6 7}{7})

d o main f (x) = x^{2} + 3 x

mi d p o in t (- 1, 1), (7, - 3)

d o main f (x) = - 2 x^{2} + 3 x

cr i t i c a l f (x) = 2 x^{3} + 3 x^{2} - 36 x + 20

s hi f t f (x) = 2 sin (2 x + π) + 3