What is the inflection f(x)=sin(x/2) ?

The inflection f(x)=sin(x/2) is (4pin,0),(2pi+4pin,0)

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inflection f(x)=sin(x/2)

inflection points

f (x) = sin (\frac{x}{2})

(4 πn, 0), (2 π + 4 πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 4 πn, x = 2 π + 4 πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

sin (\frac{x}{2}) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = 4 πn, x = 2 π + 4 πn

Find intervals:

Concave Downward

: 4 πn < x < 2 π + 4 πn,

Concave Upward

: 2 π + 4 πn < x < 4 π + 4 πn

Plug

x = 4 πn

into

sin (\frac{x}{2}) : 0

(4 πn, 0)

Plug

x = 2 π + 4 πn

into

sin (\frac{x}{2}) : 0

(2 π + 4 πn, 0)

(4 πn, 0), (2 π + 4 πn, 0)

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

f (x) = - x + 2

\frac{x ^{2} + 3 x + 2}{- 3 x - 12}

2^{x - 1} + 2

f (x) = - x + 2 + 3

What is the inflection f(x)=sin(x/2) ?
The inflection f(x)=sin(x/2) is (4pin,0),(2pi+4pin,0)