What is the inflection 3/4*(x^2-1)^{2/3} ?

The inflection 3/4*(x^2-1)^{2/3} is (-sqrt(3), 3/(2*2^{1/3)}),(sqrt(3), 3/(2*2^{1/3)})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

inflection 3/4*(x^2-1)^{2/3}

inflection points

\frac{3}{4} \cdot (x^{2} - 1)^{\frac{2}{3}}

(- 3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}}), (3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}})

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < - 3,

Concave Downward

: - 3 < x < - 1,

Concave Downward

: - 1 < x < 1,

Concave Downward

: 1 < x < 3,

Concave Upward

: 3 < x < \infty

Plug

x = - 3

into

\frac{3}{4} \cdot (x^{2} - 1)^{\frac{2}{3}} : \frac{3}{2 \cdot 2 ^{\frac{1}{3}}}

(- 3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}})

Plug

x = 3

into

\frac{3}{4} \cdot (x^{2} - 1)^{\frac{2}{3}} : \frac{3}{2 \cdot 2 ^{\frac{1}{3}}}

(3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}})

(- 3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}}), (3, \frac{3}{2 \cdot 2 ^{\frac{1}{3}}})

What is the inflection 3/4*(x^2-1)^{2/3} ?
The inflection 3/4*(x^2-1)^{2/3} is (-sqrt(3), 3/(2*2^{1/3)}),(sqrt(3), 3/(2*2^{1/3)})