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

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

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

inflection points

f (x) = 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) = \frac{x - 6}{x}

f (x) = e^{3 x + 7}

f (x) = \frac{( 8 e ^{x} )}{e ^{x} - 2}

f (x) = \frac{1}{5} x + 1

2 x + 3

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