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

The inflection f(x)=sin^2(2x) is (pi/8+pi/2 n, 1/2),((3pi)/8+pi/2 n, 1/2)

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

inflection points

f (x) = sin^{2} (2 x)

(\frac{π}{8} + \frac{π}{2} n, \frac{1}{2}), (\frac{3 π}{8} + \frac{π}{2} n, \frac{1}{2})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

sin^{2} (2 x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

Find intervals:

Concave Upward

: \frac{π}{2} n \leq x < \frac{π}{8} + \frac{π}{2} n,

Concave Downward

: \frac{π}{8} + \frac{π}{2} n < x < \frac{3 π}{8} + \frac{π}{2} n,

Concave Upward

: \frac{3 π}{8} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Plug

x = \frac{π}{8} + \frac{π}{2} n

into

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

(\frac{π}{8} + \frac{π}{2} n, \frac{1}{2})

Plug

x = \frac{3 π}{8} + \frac{π}{2} n

into

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

(\frac{3 π}{8} + \frac{π}{2} n, \frac{1}{2})

(\frac{π}{8} + \frac{π}{2} n, \frac{1}{2}), (\frac{3 π}{8} + \frac{π}{2} n, \frac{1}{2})

4 y + 5 = - 7

f (x) = 7 cos (\frac{π}{2} x)

(0, 5), (- 3, 0)

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

What is the inflection f(x)=sin^2(2x) ?
The inflection f(x)=sin^2(2x) is (pi/8+pi/2 n, 1/2),((3pi)/8+pi/2 n, 1/2)