What is the inflection sin(2x) ?

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

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inflection sin(2x)

inflection points

sin (2 x)

(πn, 0), (\frac{π}{2} + πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = πn, x = \frac{π}{2} + πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

sin (2 x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = πn, x = \frac{π}{2} + πn

Find intervals:

Concave Downward

: πn < x < \frac{π}{2} + πn,

Concave Upward

: \frac{π}{2} + πn < x < π + πn

Plug

x = πn

into

sin (2 x) : 0

(πn, 0)

Plug

x = \frac{π}{2} + πn

into

sin (2 x) : 0

(\frac{π}{2} + πn, 0)

(πn, 0), (\frac{π}{2} + πn, 0)

2 x (x - 1)

f (x) = - 16 t^{2} + 64 t + 720

y = 4 x + 6

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

- x - 3