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

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

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

inflection points

\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})

\frac{10}{1 - x}

f (x) = x^{11}

\frac{( 3 e ^{x} )}{3 e ^{x} + 7}

f (x) = lo g_{4} (x)

f (x) = \frac{4 x ^{2} - 5}{2 x ^{2} + 8}

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