What is the inflection 3cos(x) ?

The inflection 3cos(x) is (pi/2+2pin,0),((3pi)/2+2pin,0)

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inflection 3cos(x)

inflection points

3 cos (x)

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

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

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

All inflection points are in domain and not on domain edges

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Find intervals:

Concave Downward

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Concave Upward

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

Concave Downward

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

Plug

x = \frac{π}{2} + 2 πn

into

3 cos (x) : 0

(\frac{π}{2} + 2 πn, 0)

Plug

x = \frac{3 π}{2} + 2 πn

into

3 cos (x) : 0

(\frac{3 π}{2} + 2 πn, 0)

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

f (x) = x^{3} - 5 x

f (x) = \frac{3}{x} + 6

x^{2} - 4 x + 5

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

f (x) = 3 - 3 e^{x}

What is the inflection 3cos(x) ?
The inflection 3cos(x) is (pi/2+2pin,0),((3pi)/2+2pin,0)