What is the inflection f(x)=(x^3)/(x^2+5) ?

The inflection f(x)=(x^3)/(x^2+5) is (-sqrt(15),-(3sqrt(15))/4),(0,0),(sqrt(15),(3sqrt(15))/4)

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inflection f(x)=(x^3)/(x^2+5)

inflection points

f (x) = \frac{x ^{3}}{x ^{2} + 5}

(- 15, - \frac{3 15}{4}), (0, 0), (15, \frac{3 15}{4})

Solution steps

f^{''} (x) = \frac{10 x ( - x ^{2} + 15 )}{( x ^{2} + 5 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - 15,

Concave Downward

: - 15 < x < 0,

Concave Upward

: 0 < x < 15,

Concave Downward

: 15 < x < \infty

Plug

x = - 15

into

\frac{x ^{3}}{x ^{2} + 5} : - \frac{3 15}{4}

(- 15, - \frac{3 15}{4})

Plug

x = 0

into

\frac{x ^{3}}{x ^{2} + 5} : 0

(0, 0)

Plug

x = 15

into

\frac{x ^{3}}{x ^{2} + 5} : \frac{3 15}{4}

(15, \frac{3 15}{4})

(- 15, - \frac{3 15}{4}), (0, 0), (15, \frac{3 15}{4})

in t erce pt s f (x) = - \frac{3}{2}

r an g e f (x) = \frac{x - 2}{x - 1}

in t erce pt s - 5 p^{2} + 15000 p

d i s t an ce (- 2, - 6), (3, - 5)

in v erse f (x) = ln (x)

What is the inflection f(x)=(x^3)/(x^2+5) ?
The inflection f(x)=(x^3)/(x^2+5) is (-sqrt(15),-(3sqrt(15))/4),(0,0),(sqrt(15),(3sqrt(15))/4)