What is the inflection sin^2(x) ?

The inflection sin^2(x) is (pi/4+pin, 1/2),((3pi)/4+pin, 1/2)

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inflection sin^2(x)

inflection points

sin^{2} (x)

(\frac{π}{4} + πn, \frac{1}{2}), (\frac{3 π}{4} + πn, \frac{1}{2})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + 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 = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Find intervals:

Concave Upward

: πn \leq x < \frac{π}{4} + πn,

Concave Downward

: \frac{π}{4} + πn < x < \frac{3 π}{4} + πn,

Concave Upward

: \frac{3 π}{4} + πn < x < π + πn

Plug

x = \frac{π}{4} + πn

into

sin^{2} (x) : \frac{1}{2}

(\frac{π}{4} + πn, \frac{1}{2})

Plug

x = \frac{3 π}{4} + πn

into

sin^{2} (x) : \frac{1}{2}

(\frac{3 π}{4} + πn, \frac{1}{2})

(\frac{π}{4} + πn, \frac{1}{2}), (\frac{3 π}{4} + πn, \frac{1}{2})

f (x) = x - 3

f (x) = \frac{4 x ^{2} + 1}{2 x ^{2} - 9}

- 4 x + 3

f (x) = 3 x + 2

e^{x}

What is the inflection sin^2(x) ?
The inflection sin^2(x) is (pi/4+pin, 1/2),((3pi)/4+pin, 1/2)