en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inflection y=(-x^2)/(x^2-2x+8)

Solution

inflection points

y = \frac{- x ^{2}}{x ^{2} - 2 x + 8}

Solution

(- 1.53746 \dots, - 0.17589 \dots), (1.76850 \dots, - 0.41203 \dots), (11.76896 \dots, - 1.12635 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x \approx - 1.53746 \dots, x \approx 1.76850 \dots, x = 11.76896 \dots

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

\frac{- x ^{2}}{x ^{2} - 2 x + 8} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x \approx - 1.53746 \dots, x \approx 1.76850 \dots, x = 11.76896 \dots

Find intervals:

Concave Upward

: - \infty < x < - 1.53746 \dots,

Concave Downward

: - 1.53746 \dots < x < 1.76850 \dots,

Concave Upward

: 1.76850 \dots < x < 11.76896 \dots,

Concave Downward

: 11.76896 \dots < x < \infty

Plug

x = - 1.53746 \dots

into

\frac{- x ^{2}}{x ^{2} - 2 x + 8} : - 0.17589 \dots

(- 1.53746 \dots, - 0.17589 \dots)

Plug

x = 1.76850 \dots

into

\frac{- x ^{2}}{x ^{2} - 2 x + 8} : - 0.41203 \dots

(1.76850 \dots, - 0.41203 \dots)

Plug

x = 11.76896 \dots

into

\frac{- x ^{2}}{x ^{2} - 2 x + 8} : - 1.12635 \dots

(11.76896 \dots, - 1.12635 \dots)

(- 1.53746 \dots, - 0.17589 \dots), (1.76850 \dots, - 0.41203 \dots), (11.76896 \dots, - 1.12635 \dots)

Popular Examples

inverse of y=ln(x-2)inverse

y = ln (x - 2)

domain of f(x)=(4x+5)/(x^2-x+1)domain

f (x) = \frac{4 x + 5}{x ^{2} - x + 1}

range of 5ln(x)range

5 ln (x)

inverse of f(x)=(x+3)^2 inverse

f (x) = (x + 3)^{2}

critical f(x)=x^2e^{(18x)}critical points

f (x) = x^{2} e^{(18 x)}