What is the inflection f(x)=3+4x^2-1/2 x^4 ?

The inflection f(x)=3+4x^2-1/2 x^4 is (-2/(sqrt(3)), 67/9),(2/(sqrt(3)), 67/9)

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inflection f(x)=3+4x^2-1/2 x^4

inflection points

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

(- \frac{2}{3}, \frac{67}{9}), (\frac{2}{3}, \frac{67}{9})

Solution steps

f^{''} (x) = - 6 x^{2} + 8

Find intervals:

Concave Downward

: - \infty < x < - \frac{2}{3},

Concave Upward

: - \frac{2}{3} < x < \frac{2}{3},

Concave Downward

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

3 + 4 x^{2} - \frac{1}{2} x^{4} : \frac{67}{9}

(- \frac{2}{3}, \frac{67}{9})

Plug

x = \frac{2}{3}

into

3 + 4 x^{2} - \frac{1}{2} x^{4} : \frac{67}{9}

(\frac{2}{3}, \frac{67}{9})

(- \frac{2}{3}, \frac{67}{9}), (\frac{2}{3}, \frac{67}{9})

What is the inflection f(x)=3+4x^2-1/2 x^4 ?
The inflection f(x)=3+4x^2-1/2 x^4 is (-2/(sqrt(3)), 67/9),(2/(sqrt(3)), 67/9)