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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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})

f (x) = x^{3} - 1

x - 2 y = 2

y = 2 x + 7

f (x) = y^{2}

f (x) = 8 x - 18

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)