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

The inflection x/(x^2-3x-4) is (0.93244…,-0.15729…)

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

inflection points

\frac{x}{x ^{2} - 3 x - 4}

(0.93244 \dots, - 0.15729 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x \approx 0.93244 \dots, x = - 1, x = 4

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

\frac{x}{x ^{2} - 3 x - 4} : x < - 1 or - 1 < x < 4 or x > 4

f (x)

is not defined at

x = - 1, x = 4

, therefore:

x \approx 0.93244 \dots

Find intervals:

Concave Downward

: - \infty < x < - 1,

Concave Upward

: - 1 < x < 0.93244 \dots,

Concave Downward

: 0.93244 \dots < x < 4,

Concave Upward

: 4 < x < \infty

Plug

x = 0.93244 \dots

into

\frac{x}{x ^{2} - 3 x - 4} : - 0.15729 \dots

(0.93244 \dots, - 0.15729 \dots)

f (x) = x^{2} - 8 x + 16

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

f (x) = x^{3} - x

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

x + 6

What is the inflection x/(x^2-3x-4) ?
The inflection x/(x^2-3x-4) is (0.93244…,-0.15729…)