What is the inflection f(x)=(x-4)/(3x-x^2) ?

The inflection f(x)=(x-4)/(3x-x^2) is (8.10724…,-0.09919…)

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inflection f(x)=(x-4)/(3x-x^2)

inflection points

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

(8.10724 \dots, - 0.09919 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x \approx 8.10724 \dots, x = 0, x = 3

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

\frac{x - 4}{3 x - x ^{2}} : x < 0 or 0 < x < 3 or x > 3

f (x)

is not defined at

x = 0, x = 3

, therefore:

x \approx 8.10724 \dots

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 3,

Concave Upward

: 3 < x < 8.10724 \dots,

Concave Downward

: 8.10724 \dots < x < \infty

Plug

x = 8.10724 \dots

into

\frac{x - 4}{3 x - x ^{2}} : - 0.09919 \dots

(8.10724 \dots, - 0.09919 \dots)

What is the inflection f(x)=(x-4)/(3x-x^2) ?
The inflection f(x)=(x-4)/(3x-x^2) is (8.10724…,-0.09919…)