What is the inflection f(x)=ln(x^2-4x+5) ?

The inflection f(x)=ln(x^2-4x+5) is (1,ln(2)),(3,ln(2))

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inflection f(x)=ln(x^2-4x+5)

inflection points

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

(1, ln (2)), (3, ln (2))

Solution steps

f^{''} (x) = \frac{- 2 x ^{2} + 8 x - 6}{( x ^{2} - 4 x + 5 ) ^{2}}

Find intervals:

Concave Downward

: - \infty < x < 1,

Concave Upward

: 1 < x < 3,

Concave Downward

: 3 < x < \infty

Plug

x = 1

into

ln (x^{2} - 4 x + 5) : ln (2)

(1, ln (2))

Plug

x = 3

into

ln (x^{2} - 4 x + 5) : ln (2)

(3, ln (2))

(1, ln (2)), (3, ln (2))

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

f (x) = \frac{- 3 x ^{2} - 12 x}{5 x ^{2}}

(1, 4), (0, - 2)

f (x) = x + 4

- 3 x + 7

What is the inflection f(x)=ln(x^2-4x+5) ?
The inflection f(x)=ln(x^2-4x+5) is (1,ln(2)),(3,ln(2))