What is the inflection x/(x^2+10x+24) ?

The inflection x/(x^2+10x+24) is (9.82033…,0.04491…)

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inflection x/(x^2+10x+24)

inflection points

\frac{x}{x ^{2} + 10 x + 24}

(9.82033 \dots, 0.04491 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 9.82033 \dots, x = - 6, x = - 4

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

\frac{x}{x ^{2} + 10 x + 24} : x < - 6 or - 6 < x < - 4 or x > - 4

f (x)

is not defined at

x = - 6, x = - 4

, therefore:

x = 9.82033 \dots

Find intervals:

Concave Downward

: - \infty < x < - 6,

Concave Upward

: - 6 < x < - 4,

Concave Downward

: - 4 < x < 9.82033 \dots,

Concave Upward

: 9.82033 \dots < x < \infty

Plug

x = 9.82033 \dots

into

\frac{x}{x ^{2} + 10 x + 24} : 0.04491 \dots

(9.82033 \dots, 0.04491 \dots)

What is the inflection x/(x^2+10x+24) ?
The inflection x/(x^2+10x+24) is (9.82033…,0.04491…)