What is the inflection (8x)/((5x^2+4)^2) ?

The inflection (8x)/((5x^2+4)^2) is (-2/(sqrt(5)),-1/(4sqrt(5))),(0,0),(2/(sqrt(5)), 1/(4sqrt(5)))

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inflection (8x)/((5x^2+4)^2)

inflection points

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

(- \frac{2}{5}, - \frac{1}{4 5}), (0, 0), (\frac{2}{5}, \frac{1}{4 5})

Solution steps

f^{''} (x) = - \frac{480 x ( - 5 x ^{2} + 4 )}{( 5 x ^{2} + 4 ) ^{4}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{2}{5},

Concave Upward

: - \frac{2}{5} < x < 0,

Concave Downward

: 0 < x < \frac{2}{5},

Concave Upward

: \frac{2}{5} < x < \infty

Plug

x = - \frac{2}{5}

into

\frac{8 x}{( 5 x ^{2} + 4 ) ^{2}} : - \frac{1}{4 5}

(- \frac{2}{5}, - \frac{1}{4 5})

Plug

x = 0

into

\frac{8 x}{( 5 x ^{2} + 4 ) ^{2}} : 0

(0, 0)

Plug

x = \frac{2}{5}

into

\frac{8 x}{( 5 x ^{2} + 4 ) ^{2}} : \frac{1}{4 5}

(\frac{2}{5}, \frac{1}{4 5})

(- \frac{2}{5}, - \frac{1}{4 5}), (0, 0), (\frac{2}{5}, \frac{1}{4 5})

f (x) = - \frac{1}{x - 3} + 2

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

(- 4, 5), (2, - 3)

\frac{1}{x + 10}

f (x) = \frac{2}{3} x - 4

What is the inflection (8x)/((5x^2+4)^2) ?
The inflection (8x)/((5x^2+4)^2) is (-2/(sqrt(5)),-1/(4sqrt(5))),(0,0),(2/(sqrt(5)), 1/(4sqrt(5)))