What is the inflection (x-1)/((x+3)(x-2)) ?

The inflection (x-1)/((x+3)(x-2)) is (0.06755…,0.15729…)

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inflection (x-1)/((x+3)(x-2))

inflection points

\frac{x - 1}{( x + 3 ) ( x - 2 )}

(0.06755 \dots, 0.15729 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x \approx 0.06755 \dots, x = - 3, x = 2

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

\frac{x - 1}{( x + 3 ) ( x - 2 )} : x < - 3 or - 3 < x < 2 or x > 2

f (x)

is not defined at

x = - 3, x = 2

, therefore:

x \approx 0.06755 \dots

Find intervals:

Concave Downward

: - \infty < x < - 3,

Concave Upward

: - 3 < x < 0.06755 \dots,

Concave Downward

: 0.06755 \dots < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = 0.06755 \dots

into

\frac{x - 1}{( x + 3 ) ( x - 2 )} : 0.15729 \dots

(0.06755 \dots, 0.15729 \dots)

f (x) = \frac{2 x ^{2} - 5 x + 7}{x - 2}

(- 5, - 10), (- 1, 5)

f (x) = 2 x - 4 y = 9

(- 5 - 6), (- 5 - 1)

x - 4 + 5

What is the inflection (x-1)/((x+3)(x-2)) ?
The inflection (x-1)/((x+3)(x-2)) is (0.06755…,0.15729…)