What is the inflection sin(x) ?

The inflection sin(x) is (2pin,0),(pi+2pin,0)

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inflection sin(x)

inflection points

sin (x)

(2 πn, 0), (π + 2 πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 2 πn, x = π + 2 πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

sin (x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = 2 πn, x = π + 2 πn

Find intervals:

Concave Downward

: 2 πn < x < π + 2 πn,

Concave Upward

: π + 2 πn < x < 2 π + 2 πn

Plug

x = 2 πn

into

sin (x) : 0

(2 πn, 0)

Plug

x = π + 2 πn

into

sin (x) : 0

(π + 2 πn, 0)

(2 πn, 0), (π + 2 πn, 0)

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

\frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}}

- 2 sin (2 x + \frac{2 π}{5}) + 3

f (x) = \frac{5 x + 1}{2 x ^{2} - 2 x - 12}

y = 0.8 x + 8.7