What is the inflection x/(x^2+64) ?

The inflection x/(x^2+64) is (-8sqrt(3),-(sqrt(3))/(32)),(0,0),(8sqrt(3),(sqrt(3))/(32))

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inflection x/(x^2+64)

inflection points

\frac{x}{x ^{2} + 64}

(- 83, - \frac{3}{32}), (0, 0), (83, \frac{3}{32})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 192 )}{( x ^{2} + 64 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 83,

Concave Upward

: - 83 < x < 0,

Concave Downward

: 0 < x < 83,

Concave Upward

: 83 < x < \infty

Plug

x = - 83

into

\frac{x}{x ^{2} + 64} : - \frac{3}{32}

(- 83, - \frac{3}{32})

Plug

x = 0

into

\frac{x}{x ^{2} + 64} : 0

(0, 0)

Plug

x = 83

into

\frac{x}{x ^{2} + 64} : \frac{3}{32}

(83, \frac{3}{32})

(- 83, - \frac{3}{32}), (0, 0), (83, \frac{3}{32})

f (x) = x^{4} - 2 x^{2} + 6

f (x) = lo g_{7} (x) - 7

- 4 x

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

f (x) = x^{2} - 10 x + 8

What is the inflection x/(x^2+64) ?
The inflection x/(x^2+64) is (-8sqrt(3),-(sqrt(3))/(32)),(0,0),(8sqrt(3),(sqrt(3))/(32))