What is the inflection f(x)=4cos(3x) ?

The inflection f(x)=4cos(3x) is (pi/6+(2pi)/3 n,0),(pi/2+(2pi)/3 n,0)

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inflection f(x)=4cos(3x)

inflection points

f (x) = 4 cos (3 x)

(\frac{π}{6} + \frac{2 π}{3} n, 0), (\frac{π}{2} + \frac{2 π}{3} n, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

4 cos (3 x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

Find intervals:

Concave Downward

: \frac{2 π}{3} n \leq x < \frac{π}{6} + \frac{2 π}{3} n,

Concave Upward

: \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n,

Concave Downward

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

Plug

x = \frac{π}{6} + \frac{2 π}{3} n

into

4 cos (3 x) : 0

(\frac{π}{6} + \frac{2 π}{3} n, 0)

Plug

x = \frac{π}{2} + \frac{2 π}{3} n

into

4 cos (3 x) : 0

(\frac{π}{2} + \frac{2 π}{3} n, 0)

(\frac{π}{6} + \frac{2 π}{3} n, 0), (\frac{π}{2} + \frac{2 π}{3} n, 0)

f (x) = \frac{6 x}{7 x - 3}

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

- 5 sin (x)

g (x) = \frac{2 x - 1}{x + 3}

f (x) = 2 x^{2}

What is the inflection f(x)=4cos(3x) ?
The inflection f(x)=4cos(3x) is (pi/6+(2pi)/3 n,0),(pi/2+(2pi)/3 n,0)