What is the inflection f(x)=6+2x^2-x^4 ?

The inflection f(x)=6+2x^2-x^4 is (-1/(sqrt(3)), 59/9),(1/(sqrt(3)), 59/9)

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inflection f(x)=6+2x^2-x^4

inflection points

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

(- \frac{1}{3}, \frac{59}{9}), (\frac{1}{3}, \frac{59}{9})

Solution steps

f^{''} (x) = - 12 x^{2} + 4

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{3},

Concave Upward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Downward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

6 + 2 x^{2} - x^{4} : \frac{59}{9}

(- \frac{1}{3}, \frac{59}{9})

Plug

x = \frac{1}{3}

into

6 + 2 x^{2} - x^{4} : \frac{59}{9}

(\frac{1}{3}, \frac{59}{9})

(- \frac{1}{3}, \frac{59}{9}), (\frac{1}{3}, \frac{59}{9})

f (x) = \frac{( 16 x ^{2} - 8 x + 1 )}{4 x - 3}

f (x) = 16 - t

f (x) = \frac{e ^{x^{8}}}{2}

f (x) = \frac{( 3 x + 1 )}{( 4 x + 2 )}

\frac{x + 1}{( x + 2 ) ^{2}}

What is the inflection f(x)=6+2x^2-x^4 ?
The inflection f(x)=6+2x^2-x^4 is (-1/(sqrt(3)), 59/9),(1/(sqrt(3)), 59/9)