What is the inflection (-x^2)/(x^2-2x+8) ?

The inflection (-x^2)/(x^2-2x+8) is (-1.53746…,-0.17589…),(1.76850…,-0.41203…),(11.76896…,-1.12635…)

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

inflection points

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

(- 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)

f (x) = x + 2 - 1

x^{2} - 3 x + 7

\frac{x - 1}{x ^{3}}

f (x) = 4 x - 8

What is the inflection (-x^2)/(x^2-2x+8) ?
The inflection (-x^2)/(x^2-2x+8) is (-1.53746…,-0.17589…),(1.76850…,-0.41203…),(11.76896…,-1.12635…)