What is the inflection 2sin(2x)+3 ?

The inflection 2sin(2x)+3 is (pin,3),(pi/2+pin,3)

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inflection 2sin(2x)+3

inflection points

2 sin (2 x) + 3

(πn, 3), (\frac{π}{2} + πn, 3)

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

2 sin (2 x) + 3 : - \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

2 sin (2 x) + 3 : 3

(πn, 3)

Plug

x = \frac{π}{2} + πn

into

2 sin (2 x) + 3 : 3

(\frac{π}{2} + πn, 3)

(πn, 3), (\frac{π}{2} + πn, 3)

f (x) = \frac{4 x ^{2} - 1}{6 x + 3}

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

f (x) = 2 (x - 1)^{2} - 5

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

\frac{5}{x ^{2} + 1}

What is the inflection 2sin(2x)+3 ?
The inflection 2sin(2x)+3 is (pin,3),(pi/2+pin,3)