What is the inflection (x^2-7)^3 ?

The inflection (x^2-7)^3 is (-sqrt(7),0),(-sqrt(7/5),-21952/125),(sqrt(7/5),-21952/125),(sqrt(7),0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inflection (x^2-7)^3

inflection points

(x^{2} - 7)^{3}

(- 7, 0), (- \frac{7}{5}, - \frac{21952}{125}), (\frac{7}{5}, - \frac{21952}{125}), (7, 0)

Solution steps

f^{''} (x) = 6 (5 x^{4} - 42 x^{2} + 49)

Find intervals:

Concave Upward

: - \infty < x < - 7,

Concave Downward

: - 7 < x < - \frac{7}{5},

Concave Upward

: - \frac{7}{5} < x < \frac{7}{5},

Concave Downward

: \frac{7}{5} < x < 7,

Concave Upward

: 7 < x < \infty

Plug

x = - 7

into

(x^{2} - 7)^{3} : 0

(- 7, 0)

Plug

x = - \frac{7}{5}

into

(x^{2} - 7)^{3} : - \frac{21952}{125}

(- \frac{7}{5}, - \frac{21952}{125})

Plug

x = \frac{7}{5}

into

(x^{2} - 7)^{3} : - \frac{21952}{125}

(\frac{7}{5}, - \frac{21952}{125})

Plug

x = 7

into

(x^{2} - 7)^{3} : 0

(7, 0)

(- 7, 0), (- \frac{7}{5}, - \frac{21952}{125}), (\frac{7}{5}, - \frac{21952}{125}), (7, 0)

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

y = (x + 2)^{2}

x^{3} - 6 x^{2} - 15 x + 3

f (x) = \frac{4}{x - 5}

\frac{1}{x ^{3} + 4 x}

What is the inflection (x^2-7)^3 ?
The inflection (x^2-7)^3 is (-sqrt(7),0),(-sqrt(7/5),-21952/125),(sqrt(7/5),-21952/125),(sqrt(7),0)